Finite Group Databasebeta

C2×C8×#10621872 #25062168

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C8×#10621872

Splittings

FittingC2×C82×C43 ⋊ C2
SylowC43 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D43
commutatorC2×C43C22×C4×C8
FrattiniC42C23×D43
FittingC2×C82×C43C2
socleC23×C43C2×C42
prime radicalC23×D43C42
cosocleC42×C43C24
hypercenterC2×C82D43
hypocenterC43C2×C8×M16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135139);