Finite Group Databasebeta

← Group #11723582

Character table — Group #11723582

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11222222222223344444444444444444444446666666668888888888888121212121212121212121212121818363636545472108
order1233333466666443333466661212121212121212121212121221212121212121212121212121212121212121212122666666666666884242488122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111-111111111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11111-1-1
χ41111111111111111111-111111111-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ51111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11
χ71111111111111-1-11111-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111111111-111-1-1-11
χ81111111111111-1-11111-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11-1-1111-1
χ92222222-22222222222202222-2-2-2-200000000-2-2222222220-2-2-2-2000000000-2-2-2-200000000000000000
χ102222222-222222-2-2222202222-2-2-2-200000000-22-2-2-2-2-2-2-2-20-2-2-2-2000000000222200000000000000000
χ112222-1-1-122-1-1-12222-1-1-122-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-122-1-1-12222-1-1-1-22-1-1-12-1-1-1-2-21111112222-1-1-1-1-1-1-22-1-1-1-2-2111111-22-1-1-1-2-2111111000000000
χ132222-1-1-122-1-1-12-2-22-1-1-122-1-1-12-1-1-122-1-1-1-1-1-12-2-2-211111122-1-1-122-1-1-1-1-1-1-2-2111-2-2111111000000000
χ142222-1-1-122-1-1-12-2-22-1-1-1-22-1-1-12-1-1-1-2-21111112-2-2-2111111-22-1-1-1-2-21111112-211122-1-1-1-1-1-1000000000
χ152222-1-1-1-22-1-1-12222-1-1-102-1-1-1-211100−i3−i3−i3i3i3i3-2-222-1-1-1-1-1-10-211100−i3−i3−i3i3i3i30-211100−i3−i3−i3i3i3i3000000000
χ162222-1-1-1-22-1-1-12222-1-1-102-1-1-1-211100i3i3i3−i3−i3−i3-2-222-1-1-1-1-1-10-211100i3i3i3−i3−i3−i30-211100i3i3i3−i3−i3−i3000000000
χ172222-1-1-1-22-1-1-12-2-22-1-1-102-1-1-1-211100−i3−i3−i3i3i3i3-22-2-21111110-211100−i3−i3−i3i3i3i302-1-1-100i3i3i3−i3−i3−i3000000000
χ182222-1-1-1-22-1-1-12-2-22-1-1-102-1-1-1-211100i3i3i3−i3−i3−i3-22-2-21111110-211100i3i3i3−i3−i3−i302-1-1-100−i3−i3−i3i3i3i3000000000
χ19222-12-1-12-12-1-1222-12-1-12-12-1-1-12-1-1-1-12-1-12-1-122-1-122-1-1-1-12-12-1-1-1-12-1-12-1-12-12-1-1-1-12-1-12-1-1000000000
χ20222-12-1-12-12-1-1222-12-1-1-2-12-1-1-12-1-111-211-21122-1-122-1-1-1-1-2-12-1-111-211-211-2-12-1-111-211-211000000000
χ21222-12-1-12-12-1-12-2-2-12-1-12-12-1-1-12-1-1-1-12-1-12-1-12-211-2-211112-12-1-1-1-12-1-12-1-1-21-21111-211-211000000000
χ22222-12-1-12-12-1-12-2-2-12-1-1-2-12-1-1-12-1-111-211-2112-211-2-21111-2-12-1-111-211-21121-211-1-12-1-12-1-1000000000
χ23222-12-1-1-2-12-1-1222-12-1-10-12-1-11-211−i3i30−i3i30−i3i3-2-2-1-122-1-1-1-101-211−i3i30−i3i30−i3i301-211−i3i30−i3i30−i3i3000000000
χ24222-12-1-1-2-12-1-1222-12-1-10-12-1-11-211i3−i30i3−i30i3−i3-2-2-1-122-1-1-1-101-211i3−i30i3−i30i3−i301-211i3−i30i3−i30i3−i3000000000
χ25222-12-1-1-2-12-1-12-2-2-12-1-10-12-1-11-211−i3i30−i3i30−i3i3-2211-2-2111101-211−i3i30−i3i30−i3i30-12-1-1i3−i30i3−i30i3−i3000000000
χ26222-12-1-1-2-12-1-12-2-2-12-1-10-12-1-11-211i3−i30i3−i30i3−i3-2211-2-2111101-211i3−i30i3−i30i3−i30-12-1-1−i3i30−i3i30−i3i3000000000
χ27222-1-12-12-1-12-1222-1-12-12-1-12-1-1-12-1-1-1-12-1-1-1222-1-1-1-122-1-12-1-12-1-1-1-12-1-1-122-1-12-1-1-1-12-1-1-12000000000
χ28222-1-12-12-1-12-1222-1-12-1-2-1-12-1-1-12-1111-2111-222-1-1-1-122-1-1-2-1-12-1111-2111-2-2-1-12-1111-2111-2000000000
χ29222-1-12-12-1-12-12-2-2-1-12-12-1-12-1-1-12-1-1-1-12-1-1-122-21111-2-2112-1-12-1-1-1-12-1-1-12-211-21111-2111-2000000000
χ30222-1-12-12-1-12-12-2-2-1-12-1-2-1-12-1-1-12-1111-2111-22-21111-2-211-2-1-12-1111-2111-2211-21-1-1-12-1-1-12000000000
χ31222-1-12-1-2-1-12-1222-1-12-10-1-12-111-21−i3i3i30−i3−i3i30-2-2-1-1-1-122-1-1011-21−i3i3i30−i3−i3i30011-21−i3i3i30−i3−i3i30000000000
χ32222-1-12-1-2-1-12-1222-1-12-10-1-12-111-21i3−i3−i30i3i3−i30-2-2-1-1-1-122-1-1011-21i3−i3−i30i3i3−i30011-21i3−i3−i30i3i3−i30000000000
χ33222-1-12-1-2-1-12-12-2-2-1-12-10-1-12-111-21−i3i3i30−i3−i3i30-221111-2-211011-21−i3i3i30−i3−i3i300-1-12-1i3−i3−i30i3i3−i30000000000
χ34222-1-12-1-2-1-12-12-2-2-1-12-10-1-12-111-21i3−i3−i30i3i3−i30-221111-2-211011-21i3−i3−i30i3i3−i300-1-12-1−i3i3i30−i3−i3i30000000000
χ35222-1-1-122-1-1-12222-1-1-122-1-1-12-1-1-12-1-1-1-12-12-122-1-1-1-1-1-1222-1-1-12-1-1-1-12-12-12-1-1-12-1-1-1-12-12-1000000000
χ36222-1-1-122-1-1-12222-1-1-12-2-1-1-12-1-1-121111-21-2122-1-1-1-1-1-122-2-1-1-121111-21-21-2-1-1-121111-21-21000000000
χ37222-1-1-122-1-1-122-2-2-1-1-122-1-1-12-1-1-12-1-1-1-12-12-12-2111111-2-22-1-1-12-1-1-1-12-12-1-2111-21111-21-21000000000
χ38222-1-1-122-1-1-122-2-2-1-1-12-2-1-1-12-1-1-121111-21-212-2111111-2-2-2-1-1-121111-21-212111-2-1-1-1-12-12-1000000000
χ39222-1-1-12-2-1-1-12222-1-1-120-1-1-12111-2−i3i3−i3i30i30−i3-2-2-1-1-1-1-1-1220111-2−i3i3−i3i30i30−i30111-2−i3i3−i3i30i30−i3000000000
χ40222-1-1-12-2-1-1-12222-1-1-120-1-1-12111-2i3−i3i3−i30−i30i3-2-2-1-1-1-1-1-1220111-2i3−i3i3−i30−i30i30111-2i3−i3i3−i30−i30i3000000000
χ41222-1-1-12-2-1-1-122-2-2-1-1-120-1-1-12111-2−i3i3−i3i30i30−i3-22111111-2-20111-2−i3i3−i3i30i30−i30-1-1-12i3−i3i3−i30−i30i3000000000
χ42222-1-1-12-2-1-1-122-2-2-1-1-120-1-1-12111-2i3−i3i3−i30−i30i3-22111111-2-20111-2i3−i3i3−i30−i30i30-1-1-12−i3i3−i3i30i30−i3000000000
χ4322-1222222222-100-1-1-1-12-1-1-1-1222222222222-1000000000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000222-1-100-10
χ4422-1222222222-100-1-1-1-12-1-1-1-1222222222222-1000000000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-2-2110010
χ4522-1222222222-100-1-1-1-1-2-1-1-1-12222-2-2-2-2-2-2-2-2-10000000001-1-1-1-111111111000000000000022-2-1-10010
χ4622-1222222222-100-1-1-1-1-2-1-1-1-12222-2-2-2-2-2-2-2-2-10000000001-1-1-1-1111111110000000000000-2-221100-10
χ472-2222220-2-2-2-2-22i−2i22220-2-2-2-2000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002−202−2−i2i200
χ482-2222220-2-2-2-2-22i−2i22220-2-2-2-2000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−220−22i2−i200
χ492-2222220-2-2-2-2-2−2i2i22220-2-2-2-200000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002−202−2i2−i200
χ502-2222220-2-2-2-2-2−2i2i22220-2-2-2-200000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−220−22−i2i200
χ5144-24444-44444-200-2-2-2-20-2-2-2-2-4-4-4-400000000200000000002222000000000000000000000000000000
χ5244-24-2-2-244-2-2-2-200-21114-21114-2-2-244-2-2-2-2-2-2-2000000000-2-2111-2-21111110000000000000000000000
χ5344-24-2-2-244-2-2-2-200-2111-4-21114-2-2-2-4-4222222-20000000002-211122-1-1-1-1-1-10000000000000000000000
χ5444-24-2-2-2-44-2-2-2-200-21110-2111-422200−2i3−2i3−2i32i32i32i3200000000002-1-1-100i3i3i3−i3−i3−i30000000000000000000000
χ5544-24-2-2-2-44-2-2-2-200-21110-2111-4222002i32i32i3−2i3−2i3−2i3200000000002-1-1-100−i3−i3−i3i3i3i30000000000000000000000
χ5644-2-24-2-24-24-2-2-2001-21141-211-24-2-2-2-24-2-24-2-2-2000000000-21-21111-211-2110000000000000000000000
χ5744-2-24-2-24-24-2-2-2001-211-41-211-24-2-222-422-422-200000000021-211-1-12-1-12-1-10000000000000000000000
χ5844-2-24-2-2-4-24-2-2-2001-21101-2112-422−2i32i30−2i32i30−2i32i320000000000-12-1-1i3−i30i3−i30i3−i30000000000000000000000
χ5944-2-24-2-2-4-24-2-2-2001-21101-2112-4222i3−2i302i3−2i302i3−2i320000000000-12-1-1−i3i30−i3i30−i3i30000000000000000000000
χ6044-2-2-24-24-2-24-2-20011-21411-21-2-24-2-2-2-24-2-2-24-2000000000-211-21111-2111-20000000000000000000000
χ6144-2-2-24-24-2-24-2-20011-21-411-21-2-24-2222-4222-4-2000000000211-21-1-1-12-1-1-120000000000000000000000
χ6244-2-2-24-2-4-2-24-2-20011-21011-2122-42−2i32i32i30−2i3−2i32i3020000000000-1-12-1i3−i3−i30i3i3−i300000000000000000000000
χ6344-2-2-24-2-4-2-24-2-20011-21011-2122-422i3−2i3−2i302i32i3−2i3020000000000-1-12-1−i3i3i30−i3−i3i300000000000000000000000
χ6444-2-2-2-244-2-2-24-200111-24111-2-2-2-24-2-2-2-24-24-2-2000000000-2111-21111-21-210000000000000000000000
χ6544-2-2-2-244-2-2-24-200111-2-4111-2-2-2-242222-42-42-20000000002111-2-1-1-1-12-12-10000000000000000000000
χ6644-2-2-2-24-4-2-2-24-200111-20111-2222-4−2i32i3−2i32i302i30−2i320000000000-1-1-12i3−i3i3−i30−i30i30000000000000000000000
χ6744-2-2-2-24-4-2-2-24-200111-20111-2222-42i3−2i32i3−2i30−2i302i320000000000-1-1-12−i3i3−i3i30i30−i30000000000000000000000
χ684-444-2-2-20-4222-44i−4i4-2-2-20-4222000000000000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000000000000
χ694-444-2-2-20-4222-4−4i4i4-2-2-20-422200000000000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000000000000
χ704-44-24-2-202-422-44i−4i-24-2-202-42200000000000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000000000000
χ714-44-24-2-202-422-4−4i4i-24-2-202-422000000000000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000000000000
χ724-44-2-24-2022-42-44i−4i-2-24-2022-4200000000000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000000000000
χ734-44-2-24-2022-42-4−4i4i-2-24-2022-42000000000000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000000000000
χ744-44-2-2-240222-4-44i−4i-2-2-240222-400000000000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000000000000
χ754-44-2-2-240222-4-4−4i4i-2-2-240222-4000000000000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000000
χ764-4-244440-4-4-4-4200-2-2-2-20222200000000000000000000000000000000000000000000000022−220−220000
χ774-4-244440-4-4-4-4200-2-2-2-202222000000000000000000000000000000000000000000000000−222202−20000
χ788-8-48-4-4-40-8444400-422204-2-2-2000000000000000000000000000000000000000000000000000000000
χ798-8-4-48-4-404-8444002-4220-24-2-2000000000000000000000000000000000000000000000000000000000
χ808-8-4-4-48-4044-8440022-420-2-24-2000000000000000000000000000000000000000000000000000000000
χ818-8-4-4-4-480444-8400222-40-2-2-24000000000000000000000000000000000000000000000000000000000

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