Finite Group Databasebeta

C2×#19135012 #25098247

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135012

Splittings

FittingC2×C43×#344 ⋊ C2
SylowC43 ⋊ C2×#1891

Subgroups

subgroupG/H
centerC2×C4#13063295
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

1870 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171218);