Finite Group Databasebeta

C2×#19133112 #25063714

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

Aliases

direct productC2×#19133112

Splittings

FittingC2×C43×#407 ⋊ C2
SylowC43 ⋊ C2×#1507

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC23×C43C2×C22⋊C4
prime radicalC22×#13063299C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43C2×#1507
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

1898 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, 136685);