Finite Group Databasebeta

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M16×#10624382 #26042239

order11584
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×#10624382

Splittings

FittingM16×C181 ⋊ C4
SylowC181 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC4C22×#10624382
commutator, socleC2×C181C2×C42
FittingM16×C181C4
prime radicalC22×D181C2×C4
cosocleC4×D181C23
hypercenterM16#10624382
hypocenterC181C4×M16
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ M16

142 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#100×#10624382, #101×#10624382, #104×#10624382, …
maximal normal subgroup of#100×#10624382, #101×#10624382, #104×#10624382, …
maximal quotient ofM16×#13089685, #37548919, #37548922, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1509);