Finite Group Databasebeta

C2×#19135496 #25100581

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19135496

Splittings

FittingC22×#108×C43 ⋊ C2
SylowC43 ⋊ C2×#1977

Subgroups

subgroupG/H
centerC23#13063300
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#108×C43C2
socleC23×C43#121
prime radicalC23×D172C22
cosocleC22×C4×C43C24
hypercenterC22×#108D43
hypocenterC43C2×#1977
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

1566 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 173552);