Finite Group Databasebeta

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C3×C4×2−1+4⋊C3 #11919688

order1152
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3×C4×2−1+4⋊C3
unambiguous semidirect product(C4×2−1+4)⋊C32
unambiguous semidirect product(C3×C4×2−1+4)⋊C3

Splittings

FittingC3×C4×2−1+4 ⋊ C3
SylowC4×2−1+4 ⋊ C32

Subgroups

subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C32×C4
FrattiniC22C23×C3×A4
FittingC3×C4×2−1+4C3
socleC22×C3C23×A4
prime radicalC2×C3×2−1+4⋊C3C2
cosocleC2×Q8C23×C32
hypercenterC3×C4×D4A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153699);