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3−1+2×#622 #14518586

order1944
automorphism?
homologyAbelianization (H1) = C32×C8 · Schur multiplier (H2) = C3

Aliases

direct product3−1+2×#622
unambiguous semidirect product(C9×#622)⋊C3

Splittings

SylowC32×3−1+2 ⋊ C8

Subgroups

subgroupG/H
center, FrattiniC2×C3C32×#157
commutatorC33C32×C8
FittingC2×C32×3−1+2C4
socleC2×C33C32×C4
prime radicalC2×C34C3×C4
cosocleC3×C3⋊Dic3C2×C32
hypercenterC2×3−1+2#157
hypocenterC32C8×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×3−1+2

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2980);