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D32×#120 #11900250

order1152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productD32×#120

Splittings

FittingC32×#120 ⋊ C22
SylowC32 ⋊ C22×#120

Subgroups

subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32C22×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

9419 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72215068, D3×#10595278, D3×C3⋊D3×#120, …
maximal normal subgroup of#72215068, #120×GO+(4,𝔽2), D32×#120⋊C3, …
maximal quotient ofD32×#453, D3×#10595278, D3×C3⋊D3×#120, …
automorphism group ofC2×D3×Dic3, C2×#626, #63580

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134261);