Finite Group Databasebeta

C2×#19132946 #25062545

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19132946

Splittings

FittingC2×C43×#431 ⋊ C2
SylowC43 ⋊ C2×#1469

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#431C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D172C4
cosocleC22×C4×C43C24
hypercenterC2×#431D43
hypocenterC43C2×#1469
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

1346 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135516);