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C22×C3×D3×D4 #10596727

order576
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C210

Aliases

direct productC22×C3×D3×D4

Splittings

FittingC22×C32×D4 ⋊ C2
SylowC32 ⋊ C23×D4

Subgroups

subgroupG/H
centerC23×C3C22×D3
commutator, cosocleC2×C3C25×C3
FrattiniC2C24×C3×D3
FittingC22×C32×D4C2
socleC23×C32C23
hypercenterC22×C3×D4D3
hypocenterC3C23×C3×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×D4

2842 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×#70035, #11784604, C3×#70079, …
maximal normal subgroup ofC3×#70035, #11784604, C3×#70079, …
maximal quotient ofC22×C3×D3×C22⋊C4, C22×C3×D3×C4⋊C4, C2×C3×C4×D3×D4, …
automorphism group ofC7×#204, C2×C7×C3⋊C8, C7×#208, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8609);