Finite Group Databasebeta

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C4×#14582719 #25011916

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#14582719

Splittings

SylowC43 ⋊ C4×#364

Subgroups

subgroupG/H
centerC4×C8C22⋊D43
commutatorC4×C43C2×C4×C8
FrattiniC22×C8C22×D43
FittingC4×M32×C43C2
socleC22×C43C2×C4⋊C8
prime radicalC23×C43C2×M16
cosocleC22×C8×C43C23
hypercenterC4×M32D43
hypocenterC43C4×#364
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C4×M32

398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84887);