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C3×C4×D3×D4 #10595641

order576
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×C4×D3×D4

Splittings

FittingC32×C4×D4 ⋊ C2
SylowC32 ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC2×C3×C4C22×D3
commutatorC2×C3C23×C3×C4
FrattiniC22C23×C3×D3
FittingC32×C4×D4C2
socleC22×C32C24
prime radicalC2×C3×D3×D4C2
cosocleC22×C3C24×C3
hypercenterC3×C4×D4D3
hypocenterC3C2×C3×C4×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

899 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×D4⋊C8, D3×D4⋊(C3⋊C8), C3×#68167, …
maximal normal subgroup ofC3×D3×D4⋊C8, D3×D4⋊(C3⋊C8), C3×#68167, …
maximal quotient ofC3×C4×D3×C22⋊C4, C3×C4×D3×C4⋊C4, C3×C4×#67⋊C4, …
automorphism group ofC13×Dic6, C13×D12, C2×Dic3×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 7523);