Finite Group Databasebeta

C2×#19134432 #25094427

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19134432

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1764
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

1558 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, 167398);