Finite Group Databasebeta

C2×#19135299 #25099331

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19135299

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C2×#1937

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1937
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×C4×C8

1114 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 172302);