Finite Group Databasebeta

C22×C4×#10621902 #26003172

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

Aliases

direct productC22×C4×#10621902

Splittings

FittingC22×C4×Q8×C43 ⋊ C2
SylowC43 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC22×C4×Q8×C43C2
socleC24×C43C24
prime radicalC23×#10621902C2
cosocleC22×C43C26
hypercenterC22×C4×Q8D43
hypocenterC43C22×C4×#41
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

12878 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076143);