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C2×C3×#568⋊C3 #11919782

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

Aliases

direct productC2×C3×#568⋊C3
unambiguous semidirect product(C2×#568)⋊C32
unambiguous semidirect product(C2×C3×#568)⋊C3

Splittings

FittingC2×C3×#568 ⋊ C3
SylowC2×#568 ⋊ C32

Subgroups

subgroupG/H
centerC2×C3×C4C22×A4
commutator, hypocenterQ8C22×C32×C4
FrattiniC4C23×C3×A4
FittingC2×C3×#568C3
socleC22×C3C2×C4×A4
prime radicalC22×C3×#41⋊C3C2
cosocle#41C23×C32
hypercenterC2×C3×M16A4
LCSG ▷ Q8
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×M16

812 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, 153793);