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C2×#10620013 #13049175

order1296
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC2×#10620013

Splittings

derivedSU(3,𝔽2) ⋊ C2×C3

Subgroups

subgroupG/H
center, socle, hypercenterC2×C3PSU(3,𝔽2)⋊C3
commutator, cosocle, hypocenterSU(3,𝔽2)C2×C3
FrattiniC3C2×PSU(3,𝔽2)⋊C3
FittingC2×H(3,𝔽3)SL(2,𝔽3)
LCSG ▷ SU(3,𝔽2)
UCSC1 ◁ C2×C3

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 162

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2893);