Finite Group Databasebeta

C2×#19136410 #25249723

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19136410

Splittings

FittingC2×C43×#364 ⋊ C2
SylowC43 ⋊ C2×#2166

Subgroups

subgroupG/H
centerC2×C4#13063283
commutatorC2×C4×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#364C2
socleC22×C43#432
prime radicalC23×D43M16
cosocleC2×C8×C43C24
hypercenterC2×#364D43
hypocenterC43C2×#2166
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#364

538 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322694);