Finite Group Databasebeta

← Group #72268140

Character table — Group #72268140

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444666666661212121212121212121212122424242424242424242424243232323232323232484848484848484848484848484848486464646464646464646464649696969696969696
order12222244442244222244442222224444442244444444443666666644444444444444446666121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-111111111-1-111111111-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ41111111111-1-1-1-111111111-1-111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ5111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-1i−ii−ii−ii−i
χ6111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-1−ii−ii−ii−ii
χ7111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ8111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ92222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-1-1-100000000
χ102222222222-2-2-2-222222222-2-222222222-2-2-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1111100000000
χ11222222-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111111100000000
χ12222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-100000000
χ132222-2-222-2-2000022-2-222-2-20022-2-222-2-200002-2002-2000022-2-2-2-2220000000000000000000022-2-2000000000000
χ142222-2-222-2-2000022-2-222-2-20022-2-222-2-200002-2002-20000-1-11111-1-10000000000000000−i3−i3i3i3-1-111−i3−i3i3i300000000
χ152222-2-222-2-2000022-2-222-2-20022-2-222-2-200002-2002-20000-1-11111-1-10000000000000000i3i3−i3−i3-1-111i3i3−i3−i300000000
χ162222-2-2-2-222000022-2-2-2-22200-2-22222-2-20000-22002-2000022-2-2-2-22200000000000000000000-2-222000000000000
χ172222-2-2-2-222000022-2-2-2-22200-2-22222-2-20000-22002-20000-1-11111-1-10000000000000000−i3−i3i3i311-1-1i3i3−i3−i300000000
χ182222-2-2-2-222000022-2-2-2-22200-2-22222-2-20000-22002-20000-1-11111-1-10000000000000000i3i3−i3−i311-1-1−i3−i3i3i300000000
χ1922-2-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i2-2000000002i−2i000000000000-1-111-1-1111+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1-11-1i−ii−ii−ii−i00000000
χ2022-2-22-22i−2i2i−2i2-22i−2i2-22-22i−2i2i−2i2-2000000002i−2i000000000000-1-111-1-111−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1-11-1i−ii−ii−ii−i00000000
χ2122-2-22-22i−2i2i−2i-22−2i2i2-22-22i−2i2i−2i-2200000000−2i2i000000000000-1-111-1-1111+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-11-11i−ii−i−ii−ii00000000
χ2222-2-22-22i−2i2i−2i-22−2i2i2-22-22i−2i2i−2i-2200000000−2i2i000000000000-1-111-1-111−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-11-11i−ii−i−ii−ii00000000
χ2322-2-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i2-200000000−2i2i000000000000-1-111-1-1111−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1-11-1−ii−ii−ii−ii00000000
χ2422-2-22-2−2i2i−2i2i2-2−2i2i2-22-2−2i2i−2i2i2-200000000−2i2i000000000000-1-111-1-111−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1-11-1−ii−ii−ii−ii00000000
χ2522-2-22-2−2i2i−2i2i-222i−2i2-22-2−2i2i−2i2i-22000000002i−2i000000000000-1-111-1-1111−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-11-11−ii−iii−ii−i00000000
χ2622-2-22-2−2i2i−2i2i-222i−2i2-22-2−2i2i−2i2i-22000000002i−2i000000000000-1-111-1-111−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-11-11−ii−iii−ii−i00000000
χ27333333333333333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1000000001111111111111111000000000000-1-1-1-1-1-1-1-1
χ28333333333333333333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000011111111
χ2933333333333333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-13-1-1-13-1-1-1000000001-11-11-11-11-11-11-11-10000000000001111-1-1-1-1
χ3033333333333333-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-13-1-1-13-1-1-100000000-11-11-11-11-11-11-11-11000000000000-1-1-1-11111
χ3133333333333333-1-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-13-1-1-13-1-1000000001-11-11-11-11-11-11-11-1000000000000-1-1-1-11111
χ3233333333333333-1-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-13-1-1-13-1-100000000-11-11-11-11-11-11-11-110000000000001111-1-1-1-1
χ333333333333-3-3-3-333333333-3-3-1-1-1-1-1-1-1-1-3-311-1-111-1-111110000000011111111-1-1-1-1-1-1-1-1000000000000-1-111-1-111
χ343333333333-3-3-3-333333333-3-3-1-1-1-1-1-1-1-1-3-311-1-111-1-1111100000000-1-1-1-1-1-1-1-11111111100000000000011-1-111-1-1
χ353333333333-3-3-3-3-1-1-1-1-1-1-1-1113-13-13-13-11111-1-1-31-1-1-3111000000001-11-11-11-1-11-11-11-1100000000000011-1-1-1-111
χ363333333333-3-3-3-3-1-1-1-1-1-1-1-1113-13-13-13-11111-1-1-31-1-1-311100000000-11-11-11-111-11-11-11-1000000000000-1-11111-1-1
χ373333333333-3-3-3-3-1-1-1-1-1-1-1-111-13-13-13-131111-1-11-3-1-11-311000000001-11-11-11-1-11-11-11-11000000000000-1-11111-1-1
χ383333333333-3-3-3-3-1-1-1-1-1-1-1-111-13-13-13-131111-1-11-3-1-11-31100000000-11-11-11-111-11-11-11-100000000000011-1-1-1-111
χ39333333-3-3-3-333-3-33333-3-3-3-3331111-1-1-1-1-3-3111111-1-1-1-1-1-100000000iiii−i−i−i−iiiii−i−i−i−i000000000000−ii−ii−ii−ii
χ40333333-3-3-3-333-3-33333-3-3-3-3331111-1-1-1-1-3-3111111-1-1-1-1-1-100000000−i−i−i−iiiii−i−i−i−iiiii000000000000i−ii−ii−ii−i
χ41333333-3-3-3-333-3-3-1-1-1-11111-1-11-31-3-13-131111111-3-1-1-13-1-100000000i−ii−i−ii−iii−ii−i−ii−ii000000000000−ii−iii−ii−i
χ42333333-3-3-3-333-3-3-1-1-1-11111-1-11-31-3-13-131111111-3-1-1-13-1-100000000−ii−iii−ii−i−ii−iii−ii−i000000000000i−ii−i−ii−ii
χ43333333-3-3-3-333-3-3-1-1-1-11111-1-1-31-313-13-1111111-31-1-13-1-1-100000000i−ii−i−ii−iii−ii−i−ii−ii000000000000i−ii−i−ii−ii
χ44333333-3-3-3-333-3-3-1-1-1-11111-1-1-31-313-13-1111111-31-1-13-1-1-100000000−ii−iii−ii−i−ii−iii−ii−i000000000000−ii−iii−ii−i
χ45333333-3-3-3-3-3-3333333-3-3-3-3-3-31111-1-1-1-133-1-111-1-1-1-1111100000000iiii−i−i−i−i−i−i−i−iiiii000000000000−iii−i−iii−i
χ46333333-3-3-3-3-3-3333333-3-3-3-3-3-31111-1-1-1-133-1-111-1-1-1-1111100000000−i−i−i−iiiiiiiii−i−i−i−i000000000000i−i−iii−i−ii
χ47333333-3-3-3-3-3-333-1-1-1-11111111-31-3-13-13-1-1-1-111-13-1-11-31100000000i−ii−i−ii−ii−ii−iii−ii−i000000000000−iii−ii−i−ii
χ48333333-3-3-3-3-3-333-1-1-1-11111111-31-3-13-13-1-1-1-111-13-1-11-31100000000−ii−iii−ii−ii−ii−i−ii−ii000000000000i−i−ii−iii−i
χ49333333-3-3-3-3-3-333-1-1-1-1111111-31-313-13-1-1-1-1-1113-1-1-1-311100000000i−ii−i−ii−ii−ii−iii−ii−i000000000000i−i−ii−iii−i
χ50333333-3-3-3-3-3-333-1-1-1-1111111-31-313-13-1-1-1-1-1113-1-1-1-311100000000−ii−iii−ii−ii−ii−i−ii−ii000000000000−iii−ii−i−ii
χ5144-4-44-44i−4i4i−4i4-44i−4i4-44-44i−4i4i−4i4-4000000004i−4i00000000000011-1-111-1-10000000000000000-11-11−ii−ii−ii−ii00000000
χ5244-4-44-44i−4i4i−4i-44−4i4i4-44-44i−4i4i−4i-4400000000−4i4i00000000000011-1-111-1-100000000000000001-11-1−ii−iii−ii−i00000000
χ5344-4-44-4−4i4i−4i4i4-4−4i4i4-44-4−4i4i−4i4i4-400000000−4i4i00000000000011-1-111-1-10000000000000000-11-11i−ii−ii−ii−i00000000
χ5444-4-44-4−4i4i−4i4i-444i−4i4-44-4−4i4i−4i4i-44000000004i−4i00000000000011-1-111-1-100000000000000001-11-1i−ii−i−ii−ii00000000
χ5544-4-4-444i−4i−4i4i00004-4-444i−4i−4i4i0000000000000000000000001111-1-1-1-10000000000000000−i3i3i3−i3−iii−i3−3−3300000000
χ5644-4-4-444i−4i−4i4i00004-4-444i−4i−4i4i0000000000000000000000001111-1-1-1-10000000000000000i3−i3−i3i3−iii−i−333−300000000
χ5744-4-4-444i−4i−4i4i00004-4-444i−4i−4i4i000000000000000000000000-2-2-2-22222000000000000000000002i−2i−2i2i000000000000
χ5844-4-4-44−4i4i4i−4i00004-4-44−4i4i4i−4i0000000000000000000000001111-1-1-1-10000000000000000−i3i3i3−i3i−i−ii−333−300000000
χ5944-4-4-44−4i4i4i−4i00004-4-44−4i4i4i−4i0000000000000000000000001111-1-1-1-10000000000000000i3−i3−i3i3i−i−ii3−3−3300000000
χ6044-4-4-44−4i4i4i−4i00004-4-44−4i4i4i−4i000000000000000000000000-2-2-2-2222200000000000000000000−2i2i2i−2i000000000000
χ6166666666666666-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22200000000000000000000000000000000000000000000
χ626666666666-6-6-6-6-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-222222222-2-200000000000000000000000000000000000000000000
χ63666666-6-6-6-666-6-6-2-2-2-22222-2-22222-2-2-2-222-2-2-2-22222-2-22200000000000000000000000000000000000000000000
χ64666666-6-6-6-6-6-666-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-22222-2-200000000000000000000000000000000000000000000
χ656666-6-666-6-6000066-6-666-6-600-2-222-2-2220000-2200-22000000000000000000000000000000000000000000000000
χ666666-6-666-6-60000-2-222-2-222006-2-626-2-620000-2200-22000000000000000000000000000000000000000000000000
χ676666-6-666-6-60000-2-222-2-22200-262-6-262-60000-2200-22000000000000000000000000000000000000000000000000
χ686666-6-666-6-60000-2-222-2-22200-2-222-2-222004-42-2002-2004-400000000000000000000000000000000000000000000
χ696666-6-666-6-60000-2-222-2-22200-2-222-2-22200-442-2002-200-4400000000000000000000000000000000000000000000
χ706666-6-6-6-666000066-6-6-6-6660022-2-2-2-22200002-200-22000000000000000000000000000000000000000000000000
χ716666-6-6-6-6660000-2-22222-2-20022-2-2-2-222004-4-22002-200-4400000000000000000000000000000000000000000000
χ726666-6-6-6-6660000-2-22222-2-20022-2-2-2-22200-44-22002-2004-400000000000000000000000000000000000000000000
χ736666-6-6-6-6660000-2-22222-2-2002-6-26-262-600002-200-22000000000000000000000000000000000000000000000000
χ746666-6-6-6-6660000-2-22222-2-200-626-26-2-6200002-200-22000000000000000000000000000000000000000000000000
χ7566-6-66-66i−6i6i−6i6-66i−6i-22-22−2i2i−2i2i-2200000000−2i2i000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ7666-6-66-66i−6i6i−6i6-66i−6i-22-22−2i2i−2i2i-2200000000−2i2i00000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ7766-6-66-66i−6i6i−6i-66−6i6i-22-22−2i2i−2i2i2-2000000002i−2i000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ7866-6-66-66i−6i6i−6i-66−6i6i-22-22−2i2i−2i2i2-2000000002i−2i00000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ7966-6-66-6−6i6i−6i6i6-6−6i6i-22-222i−2i2i−2i-22000000002i−2i000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000
χ8066-6-66-6−6i6i−6i6i6-6−6i6i-22-222i−2i2i−2i-22000000002i−2i00000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000
χ8166-6-66-6−6i6i−6i6i-666i−6i-22-222i−2i2i−2i2-200000000−2i2i000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000
χ8266-6-66-6−6i6i−6i6i-666i−6i-22-222i−2i2i−2i2-200000000−2i2i00000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000
χ831212-12-12-121212i−12i−12i12i0000-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-1212−12i12i12i−12i0000-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ8516-1616-160000000000000000000000000000000000000000004-400004-4000000000000000000000000000000000000
χ8616-1616-16000000000000000000000000000000000000000000-22−2i32i3−2i32i3-22000000000000000000000000000000000000
χ8716-1616-16000000000000000000000000000000000000000000-222i3−2i32i3−2i3-22000000000000000000000000000000000000
χ8816-16-16160000000000000000000000000000000000000000004-40000-44000000000000000000000000000000000000
χ8916-16-1616000000000000000000000000000000000000000000-22−2i32i32i3−2i32-2000000000000000000000000000000000000
χ9016-16-1616000000000000000000000000000000000000000000-222i3−2i3−2i32i32-2000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).