Finite Group Databasebeta

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C24×#10624382 #26042360

order11584
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC24×#10624382
unambiguous semidirect productD181⋊(C23×C4)

Splittings

Fitting, socleC24×C181 ⋊ C4
derived, SylowC181 ⋊ C24×C4

Subgroups

subgroupG/H
center, hypercenterC24#10624382
commutator, hypocenterC181C24×C4
FrattiniC1G
Fitting, socleC24×C181C4
prime radicalC24×D181C2
cosocleD181C25
LCSG ▷ C181
UCSC1 ◁ C24

1362 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37548894, C22×(C2×#10624382)⋊C4, C2×C22⋊C4×#10624382, …
maximal normal subgroup of#37548894, C22×(C2×#10624382)⋊C4, C2×C22⋊C4×#10624382, …
maximal quotient ofC23×C4×#10624382, C23×C22⋊#10624382, C23×C4⋊#10624382, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1630);