Finite Group Databasebeta

C22×#14583379 #26003185

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#14583379

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C22×#520

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC23×#10621898C2
cosocleC22×C43C26
hypercenterC22×#117D43
hypocenterC43C22×#520
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#117

12270 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076156);