Finite Group Databasebeta

C2×#19134500 #25094697

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19134500

Splittings

SylowC43 ⋊ C2×#1778

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C43×#341C2
socleC23×C43C2×C4⋊C4
prime radicalC24×C43C2×Q8
cosocleC22×C4×C43C24
hypercenterC2×#341D43
hypocenterC43C2×#1778
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#341

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167668);