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C3×#78703 #11868084

order1152
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#78703

Splittings

FittingC2×C32×#100 ⋊ C2
SylowC32 ⋊ #3068

Subgroups

subgroupG/H
centerC2×C3C2×#884
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#100C2
socleC2×C32C2×#121
hypercenterC2×C3×#100D3
hypocenterC3C3×#3068
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

1025 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11671496, #72214981, #72214997
maximal normal subgroup ofC3×#11671496, #72214981, #72214997

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 102095);