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D32×#127 #11900699

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29×C4

Aliases

direct productD32×#127

Splittings

FittingC32×#127 ⋊ C22
SylowC32 ⋊ C22×#127

Subgroups

subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32C22×#127
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

6249 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊D3×#127, D32×#453, #127×GO+(4,𝔽2), …
maximal normal subgroup ofD32×#453, #127×GO+(4,𝔽2), #72225112, …
maximal quotient ofD3×C3⋊D3×#127, #127×((C3⋊D3)⋊C3)⋊C2, D32×#493, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134710);