Finite Group Databasebeta

C4×#14582689 #25011734

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#14582689

Splittings

SylowC43 ⋊ C4×#352

Subgroups

subgroupG/H
centerC2×C4#13063240
commutatorC23×C43C2×C42
FrattiniC22×D4C22×D43
FittingC4×#123×C43C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC4×#123D43
hypocenterC43C4×#352
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

576 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84705);