Finite Group Databasebeta

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3−1+2×C42⋊C3 #13047784

order1296
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C32×C4

Aliases

direct product3−1+2×C42⋊C3

Splittings

FittingC42×3−1+2 ⋊ C3
SylowC42 ⋊ C3×3−1+2

Subgroups

subgroupG/H
centerC3C32×C42⋊C3
commutator, cosocleC3×C42C33
Frattini, socleC22×C3C32×A4
FittingC42×3−1+2C3
prime radicalC32×C42⋊C3C3
hypercenter3−1+2C42⋊C3
hypocenterC42C3×3−1+2
LCSG ▷ C3×C42 ▷ C42
UCSC1 ◁ C3 ◁ 3−1+2

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1502);