Finite Group Databasebeta

C2×#19136040 #25125493

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136040

Splittings

SylowC43 ⋊ C2×#2079

Subgroups

subgroupG/H
centerC23#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#408C2
socleC23×C43#121
prime radicalC22×#41×C43C22
hypercenterC2×#408D43
hypocenterC43C2×#2079
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

950 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 198464);