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C22×D3×3−1+2 #10620108

order648
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23

Aliases

direct productC22×D3×3−1+2
unambiguous semidirect productC3⋊(C23×3−1+2)
unambiguous semidirect product(C2×C3)⋊(C22×3−1+2)

Splittings

FittingC22×C3×3−1+2 ⋊ C2
SylowC3×3−1+2 ⋊ C23

Subgroups

subgroupG/H
centerC22×C3C32×D3
commutator, cosocleC32C23×C32
FrattiniC3C22×C32×D3
FittingC22×C3×3−1+2C2
socleC22×C32C2×C32
prime radicalC22×C32×D3C3
hypercenterC22×3−1+2D3
hypocenterC3C23×3−1+2
LCSG ▷ C32 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×3−1+2

311 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D3)⋊(3−1+2⋊C4), 3−1+2×(C2×D3)⋊C4, C2×D3×3−1+2⋊C4, …
maximal normal subgroup of(C2×D3)⋊(3−1+2⋊C4), 3−1+2×(C2×D3)⋊C4, C2×D3×3−1+2⋊C4, …
maximal quotient ofC2×Dic6×3−1+2, C2×C4×D3×3−1+2, C2×D12×3−1+2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 627);