Finite Group Databasebeta

C8×#13063299 #25102625

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC8×#13063299

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C8×#121

Subgroups

subgroupG/H
centerC22×C8C22×D43
commutatorC22×C43C23×C8
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C23×C4
prime radicalC2×#13063299C4
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C8×#121
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1222 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 175596);