Finite Group Databasebeta

C4×#14583140 #25103104

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14583140

Splittings

SylowC43 ⋊ C4×#467

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C4×#467
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1054 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 176075);