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C2×A4×3−1+2 #10620098

order648
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×A4×3−1+2

Splittings

FittingC23×3−1+2 ⋊ C3
SylowC23 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC2×C3C32×A4
commutator, cosocleC22×C3C2×C33
FrattiniC3C2×C32×A4
FittingC23×3−1+2C3
socleC23×C3C33
prime radicalC2×C32×A4C3
hypercenterC2×3−1+2A4
hypocenterC22C2×C3×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 54

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×SL(2,ℤ/4), A4⋊(3−1+2⋊C4), A4×3−1+2⋊C4, …
maximal normal subgroup of3−1+2×SL(2,ℤ/4), A4⋊(3−1+2⋊C4), A4×3−1+2⋊C4, …
maximal quotient ofC4×A4×3−1+2, C2×SL(2,𝔽3)×3−1+2, 3−1+2×#41⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 617);