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D3×#942 #10595316

order576
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD3×#942

Splittings

FittingC2×C32×Q8 ⋊ C22
SylowC32 ⋊ C2×#137

Subgroups

subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC2×C32×Q8C22
socleC2×C32C22×D4
prime radicalD3×#235C2
hypercenterC2×Q8D32
hypocenterC32C2×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#5202, D3×#5061, D3×#5205, …
maximal normal subgroup ofD3×#5202, D3×#5061, D3×#5205, …
maximal quotient ofD3×#5225, D3×#4966, D3×#4964, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 7198);