Finite Group Databasebeta

C2×#19134439 #25094435

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

Aliases

direct productC2×#19134439

Splittings

FittingC22×#97×C43 ⋊ C2
SylowC43 ⋊ C2×#1765

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×#97×C43C2
socleC23×C43C4×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×#97D43
hypocenterC43C2×#1765
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C22×#97

1518 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167406);