Finite Group Databasebeta

C4×#14583616 #25256544

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

Aliases

direct productC4×#14583616

Splittings

FittingC4×#126×C43 ⋊ C2
SylowC43 ⋊ C4×#556

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#126×C43C2
socle, cosocleC23×C43C25
prime radicalC22×C22⋊D43C23
hypercenterC4×#126D43
hypocenterC43C4×#556
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#126

2340 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 329515);