Finite Group Databasebeta

C2×#19138330 #25264047

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19138330

Splittings

FittingC23×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#2443

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC23×C4⋊C4×C43C2
socleC24×C43C24
prime radicalC22×#13063299C2
hypercenterC23×C4⋊C4D43
hypocenterC43C2×#2443
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4⋊C4

4002 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 337018);