Finite Group Databasebeta

C2×#19137038 #25254936

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#19137038

Splittings

FittingC23×C42×C43 ⋊ C2
SylowC43 ⋊ C2×#2290

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC23×C42×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC23×C42D43
hypocenterC43C2×#2290
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C23×C42

4134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327907);