Finite Group Databasebeta

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C2×C8×#10624382 #26042233

order11584
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#10624382

Splittings

FittingC2×C8×C181 ⋊ C4
derived, SylowC181 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#10624382
commutator, hypocenterC181C2×C4×C8
FrattiniC4C22×#10624382
FittingC2×C8×C181C4
socleC22×C181C42
prime radicalC22×D181C2×C4
cosocleC4×D181C23
LCSG ▷ C181
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#10624382)⋊C16, #37548764, C4×C8×#10624382, …
maximal normal subgroup of(C2×#10624382)⋊C16, #37548764, C4×C8×#10624382, …
maximal quotient ofC2×C8×#13089685, C8×D181⋊C8, C2×#13089685⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1503);