Finite Group Databasebeta

C2×#19136215 #25249286

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136215

Splittings

FittingC22×M32×C43 ⋊ C2
SylowC43 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C8(C2×D43)⋊C4
commutatorC22×C43C23×C8
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC22×C43C2×C22⋊C8
prime radicalC22×#10621898C4
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×#2115
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×M32

1154 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, 322257);