Finite Group Databasebeta

C2×#19136194 #25249234

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

Aliases

direct productC2×#19136194

Splittings

SylowC43 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C8C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC2×C8C23×D43
FittingC22×M32×C43C2
socleC23×C43C22×C8
prime radicalC24×C43C2×C8
cosocleC2×C8×C43C24
hypercenterC22×M32D43
hypocenterC43C2×#2108
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C22×M32

854 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322205);