Finite Group Databasebeta

C2×#19137288 #25255351

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

Aliases

direct productC2×#19137288

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C2×#2324

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#117×C43C2
socleC24×C43C24
prime radicalC22×#13063299C2
cosocleC23×C43C25
hypercenterC22×#117D43
hypocenterC43C2×#2324
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#117

3934 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328322);