Finite Group Databasebeta

← Group #11772781

Character table — Group #11772781

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222222224444444444444448888888888888888888888888888888888881616161616161616161616161672727272144144
order12233336666444666612121212121212122444666666661212121212121212121212121212121212121212121212128121212122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111111111111-11-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111-11-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111-11-1111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−i
χ611111111111-11-1111111111111111-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii
χ711111111111-11-1111111111111-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111ii−i−i−ii
χ811111111111-11-1111111111111-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111−i−iiii−i
χ9222222222222222222222222220-20-200000000-2-2-2-2-2-2-2-200000000222222220-2-2-2-200000000000000
χ1022222222222-22-22222222222220-20200000000-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20222200000000000000
χ112222-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-10-20-200−i3−i3−i3i3i3i3111111-2-200−i3−i3−i3i3i3i322-1-1-1-1-1-10111-200−i3−i3−i3i3i3i3000000
χ122222-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-10-20-200i3i3i3−i3−i3−i3111111-2-200i3i3i3−i3−i3−i322-1-1-1-1-1-10111-200i3i3i3−i3−i3−i3000000
χ132222-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1000000
χ142222-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-1-22-22-2-2111111-1-1-1-1-1-122-2-211111122-1-1-1-1-1-1-2-1-1-12-2-2111111000000
χ152222-1-1-12-1-1-1-22-22-1-1-122-1-1-1-1-1-10-20200−i3−i3−i3i3i3i3111111-2-200−i3−i3−i3i3i3i3-2-21111110-1-1-1200i3i3i3−i3−i3−i3000000
χ162222-1-1-12-1-1-1-22-22-1-1-122-1-1-1-1-1-10-20200i3i3i3−i3−i3−i3111111-2-200i3i3i3−i3−i3−i3-2-21111110-1-1-1200−i3−i3−i3i3i3i3000000
χ172222-1-1-12-1-1-1-22-22-1-1-122-1-1-1-1-1-1222-222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2111111-2111-2-2-2111111000000
χ182222-1-1-12-1-1-1-22-22-1-1-122-1-1-1-1-1-1-22-2-2-2-2111111-1-1-1-1-1-122-2-2111111-2-21111112111-222-1-1-1-1-1-1000000
χ19222-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-10-20-2−i3i30−i3i30−i3i31111-2-211−i3i30−i3i30−i3i3-1-122-1-1-1-1011-21−i3i30−i3i30−i3i3000000
χ20222-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-10-20-2i3−i30i3−i30i3−i31111-2-211i3−i30i3−i30i3−i3-1-122-1-1-1-1011-21i3−i30i3−i30i3−i3000000
χ21222-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-12222-1-12-1-12-1-1-1-1-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-12-1-12-1-1-12-1-12-1-1000000
χ22222-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-1-22-2211-211-211-1-1-1-122-1-111-211-211-1-122-1-1-1-1-2-1-12-111-211-211000000
χ23222-12-1-1-12-1-1-22-2-12-1-1-1-122-1-1-1-10-202−i3i30−i3i30−i3i31111-2-211−i3i30−i3i30−i3i311-2-211110-1-12-1i3−i30i3−i30i3−i3000000
χ24222-12-1-1-12-1-1-22-2-12-1-1-1-122-1-1-1-10-202i3−i30i3−i30i3−i31111-2-211i3−i30i3−i30i3−i311-2-211110-1-12-1−i3i30−i3i30−i3i3000000
χ25222-12-1-1-12-1-1-22-2-12-1-1-1-122-1-1-1-1222-2-1-12-1-12-1-1-1-1-1-122-1-1-1-12-1-12-1-111-2-21111-211-2111-211-211000000
χ26222-12-1-1-12-1-1-22-2-12-1-1-1-122-1-1-1-1-22-2-211-211-211-1-1-1-122-1-111-211-21111-2-21111211-21-1-12-1-12-1-1000000
χ27222-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-10-20-2−i3i3−i3i30i30−i311-2-21111−i3i3−i3i30i30−i3-1-1-1-122-1-101-211−i3i3−i3i30i30−i3000000
χ28222-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-10-20-2i3−i3i3−i30−i30i311-2-21111i3−i3i3−i30−i30i3-1-1-1-122-1-101-211i3−i3i3−i30−i30i3000000
χ29222-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-12222-1-1-1-12-12-1-1-122-1-1-1-1-1-1-1-12-12-1-1-1-1-122-1-12-12-1-1-1-1-1-12-12-1000000
χ30222-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-1-22-221111-21-21-1-122-1-1-1-11111-21-21-1-1-1-122-1-1-2-12-1-11111-21-21000000
χ31222-1-12-1-1-12-1-22-2-1-12-1-1-1-1-122-1-10-202−i3i3−i3i30i30−i311-2-21111−i3i3−i3i30i30−i31111-2-2110-12-1-1i3−i3i3−i30−i30i3000000
χ32222-1-12-1-1-12-1-22-2-1-12-1-1-1-1-122-1-10-202i3−i3i3−i30−i30i311-2-21111i3−i3i3−i30−i30i31111-2-2110-12-1-1−i3i3−i3i30i30−i3000000
χ33222-1-12-1-1-12-1-22-2-1-12-1-1-1-1-122-1-1222-2-1-1-1-12-12-1-1-122-1-1-1-1-1-1-1-12-12-11111-2-211-21-2111111-21-21000000
χ34222-1-12-1-1-12-1-22-2-1-12-1-1-1-1-122-1-1-22-2-21111-21-21-1-122-1-1-1-11111-21-211111-2-21121-211-1-1-1-12-12-1000000
χ35222-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-1220-20-2−i3i3i30−i3−i3i30-2-2111111−i3i3i30−i3−i3i30-1-1-1-1-1-1220-2111−i3i3i30−i3−i3i30000000
χ36222-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-1220-20-2i3−i3−i30i3i3−i30-2-2111111i3−i3−i30i3i3−i30-1-1-1-1-1-1220-2111i3−i3−i30i3i3−i30000000
χ37222-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-1222222-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-12-1-1-12000000
χ38222-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-122-22-22111-2111-222-1-1-1-1-1-1111-2111-2-1-1-1-1-1-122-22-1-1-1111-2111-2000000
χ39222-1-1-12-1-1-12-22-2-1-1-12-1-1-1-1-1-1220-202−i3i3i30−i3−i3i30-2-2111111−i3i3i30−i3−i3i30111111-2-202-1-1-1i3−i3−i30i3i3−i30000000
χ40222-1-1-12-1-1-12-22-2-1-1-12-1-1-1-1-1-1220-202i3−i3−i30i3i3−i30-2-2111111i3−i3−i30i3i3−i30111111-2-202-1-1-1−i3i3i30−i3−i3i30000000
χ41222-1-1-12-1-1-12-22-2-1-1-12-1-1-1-1-1-122222-2-1-1-12-1-1-1222-1-1-1-1-1-1-1-1-12-1-1-12111111-2-2-2-2111111-2111-2000000
χ42222-1-1-12-1-1-12-22-2-1-1-12-1-1-1-1-1-122-22-2-2111-2111-222-1-1-1-1-1-1111-2111-2111111-2-22-2111-1-1-12-1-1-12000000
χ43444444444440-404444-4-4-4-4-4-4-4-40000000000000000000000000000000000000000000000000000000
χ444444-2-2-24-2-2-20-404-2-2-2-4-4222222000000000000−2i32i3−2i32i3−2i32i30000000000000000000000000000000000000
χ454444-2-2-24-2-2-20-404-2-2-2-4-42222220000000000002i3−2i32i3−2i32i3−2i30000000000000000000000000000000000000
χ46444-24-2-2-24-2-20-40-24-2-222-4-42222000000000000−2i32i32i3−2i300−2i32i300000000000000000000000000000000000
χ47444-24-2-2-24-2-20-40-24-2-222-4-422220000000000002i3−2i3−2i32i3002i3−2i300000000000000000000000000000000000
χ48444-2-24-2-2-24-20-40-2-24-22222-4-422000000000000−2i32i3002i3−2i32i3−2i300000000000000000000000000000000000
χ49444-2-24-2-2-24-20-40-2-24-22222-4-4220000000000002i3−2i300−2i32i3−2i32i300000000000000000000000000000000000
χ50444-2-2-24-2-2-240-40-2-2-24222222-4-400000000000000−2i32i32i3−2i3−2i32i300000000000000000000000000000000000
χ51444-2-2-24-2-2-240-40-2-2-24222222-4-4000000000000002i3−2i3−2i32i32i3−2i300000000000000000000000000000000000
χ5244-444444444000-4-4-4-40000000020-202222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000
χ5344-444444444000-4-4-4-400000000-2020-2-2-2-2-2-2-2-20000000022222222000000000000000000000000000
χ5444-44-2-2-24-2-2-2000-422200−2i32i3−2i32i3−2i32i320-2022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i300000000-2-21+i31+i31+i31−i31−i31−i3000000000000000000000000000
χ5544-44-2-2-24-2-2-2000-422200−2i32i3−2i32i3−2i32i3-2020-2-21+i31+i31+i31−i31−i31−i30000000022−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3000000000000000000000000000
χ5644-44-2-2-24-2-2-2000-4222002i3−2i32i3−2i32i3−2i320-2022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i300000000-2-21−i31−i31−i31+i31+i31+i3000000000000000000000000000
χ5744-44-2-2-24-2-2-2000-4222002i3−2i32i3−2i32i3−2i3-2020-2-21−i31−i31−i31+i31+i31+i30000000022−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3000000000000000000000000000
χ5844-4-24-2-2-24-2-20002-422−2i32i300−2i32i32i3−2i320-20−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000001−i31+i3-21−i31+i3-21−i31+i3000000000000000000000000000
χ5944-4-24-2-2-24-2-20002-422−2i32i300−2i32i32i3−2i3-20201−i31+i3-21−i31+i3-21−i31+i300000000−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000000
χ6044-4-24-2-2-24-2-20002-4222i3−2i3002i3−2i3−2i32i320-20−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000001+i31−i3-21+i31−i3-21+i31−i3000000000000000000000000000
χ6144-4-24-2-2-24-2-20002-4222i3−2i3002i3−2i3−2i32i3-20201+i31−i3-21+i31−i3-21+i31−i300000000−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000000
χ6244-4-2-24-2-2-24-200022-42−2i32i32i3−2i300−2i32i320-20−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3000000001−i31+i31−i31+i3-21+i3-21−i3000000000000000000000000000
χ6344-4-2-24-2-2-24-200022-42−2i32i32i3−2i300−2i32i3-20201−i31+i31−i31+i3-21+i3-21−i300000000−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3000000000000000000000000000
χ6444-4-2-24-2-2-24-200022-422i3−2i3−2i32i3002i3−2i320-20−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3000000001+i31−i31+i31−i3-21−i3-21+i3000000000000000000000000000
χ6544-4-2-24-2-2-24-200022-422i3−2i3−2i32i3002i3−2i3-20201+i31−i31+i31−i3-21−i3-21+i300000000−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3000000000000000000000000000
χ6644-4-2-2-24-2-2-24000222-4−2i32i3−2i32i32i3−2i30020-20−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32000000001−i31+i31+i3-21−i31−i31+i3-2000000000000000000000000000
χ6744-4-2-2-24-2-2-24000222-4−2i32i3−2i32i32i3−2i300-20201−i31+i31+i3-21−i31−i31+i3-200000000−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32000000000000000000000000000
χ6844-4-2-2-24-2-2-24000222-42i3−2i32i3−2i3−2i32i30020-20−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32000000001+i31−i31−i3-21+i31+i31−i3-2000000000000000000000000000
χ6944-4-2-2-24-2-2-24000222-42i3−2i32i3−2i3−2i32i300-20201+i31−i31−i3-21+i31+i31−i3-200000000−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32000000000000000000000000000
χ704-404444-4-4-4-420-200000000000000000000000000000000000000002-22-22-22-200000000000002−22−200
χ714-404444-4-4-4-420-200000000000000000000000000000000000000002-22-22-22-20000000000000−22−2200
χ724-404444-4-4-4-4-2020000000000000000000000000000000000000000-22-22-22-220000000000000−i2i2i2−i200
χ734-404444-4-4-4-4-2020000000000000000000000000000000000000000-22-22-22-220000000000000i2−i2−i2i200
χ748-808-4-4-4-844440-400000000000000000000000000000000000000004-4-22-22-220000000000000000000
χ758-808-4-4-4-8444-4040000000000000000000000000000000000000000-442-22-22-20000000000000000000
χ768-80-48-4-44-84440-40000000000000000000000000000000000000000-224-4-22-220000000000000000000
χ778-80-48-4-44-844-40400000000000000000000000000000000000000002-2-442-22-20000000000000000000
χ788-80-4-48-444-8440-40000000000000000000000000000000000000000-22-224-4-220000000000000000000
χ798-80-4-48-444-84-40400000000000000000000000000000000000000002-22-2-442-20000000000000000000
χ808-80-4-4-48444-840-40000000000000000000000000000000000000000-22-22-224-40000000000000000000
χ818-80-4-4-48444-8-40400000000000000000000000000000000000000002-22-22-2-440000000000000000000

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