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D3×#951 #10595463

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

Aliases

direct productD3×#951

Splittings

SylowC32 ⋊ C2×#137

Subgroups

subgroupG/H
centerC2C2×D3×#67
commutator, cosocleC32×C4C24
FrattiniC4C22×D32
FittingC32×#41C22
socleC2×C32C22×D4
prime radicalC3×D3×#41C2
hypercenter#41D32
hypocenterC32C2×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

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×#4825, D3×#5242, D3×#4826, …
maximal normal subgroup ofD3×#4825, D3×#5242, D3×#4826, …
maximal quotient ofD3×#5004, D3×#5232, D3×#4995, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 7345);