Finite Group Databasebeta

C2×#19133105 #25063745

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

Aliases

direct productC2×#19133105

Splittings

SylowC43 ⋊ C2×#1506

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#328D43
hypocenterC43C2×#1506
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

1130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

862 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 136716);