Finite Group Databasebeta

← Prev (#25095200) Next (#25095202) →

C4×#14583023 #25095201

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14583023

Splittings

SylowC43 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC22×C4C23×D43
FittingC4×C4⋊C8×C43C2
socle, prime radicalC23×C43C23×C4
cosocleC22×C4×C43C24
hypercenterC4×C4⋊C8D43
hypocenterC43C4×C8×Q8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168172);