Finite Group Databasebeta

C2×#19134352 #25094107

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#19134352

Splittings

FittingC2×C43×#336 ⋊ C2
SylowC43 ⋊ C2×C4×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC22×C4C23×D43
FittingC2×C43×#336C2
socleC24×C43C22×C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenterC2×#336D43
hypocenterC43C2×C4×C22⋊C8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×#336

2414 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, 167078);