Finite Group Databasebeta

← Prev (#26042162) Next (#26042164) →

C16×#10624382 #26042163

order11584
automorphism?
homologyAbelianization (H1) = C4×C16 · Schur multiplier (H2) = C4

Aliases

direct productC16×#10624382

Splittings

FittingC16×C181 ⋊ C4
derived, SylowC181 ⋊ C4×C16

Subgroups

subgroupG/H
center, hypercenterC16#10624382
commutator, hypocenterC181C4×C16
FrattiniC8C2×#10624382
FittingC16×C181C4
socleC2×C181C4×C8
prime radicalC2×D181C2×C8
cosocleC8×D181C22
LCSG ▷ C181
UCSC1 ◁ C16

58 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×#10624382, #37548827, C2×C16×#10624382, …
maximal normal subgroup ofC32×#10624382, #37548827, C2×C16×#10624382, …
maximal quotient ofC16×#13089685, #13089685⋊C16, (C2×#10624382)⋊C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1433);