Finite Group Databasebeta

C4×#14583019 #25095169

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14583019

Splittings

FittingC4×#131×C43 ⋊ C2
SylowC43 ⋊ C4×#444

Subgroups

subgroupG/H
centerC42C2×C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC4×#131×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenterC4×#131D43
hypocenterC43C4×#444
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×#131

1022 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, 168140);