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C2×C3×D3×#127 #11900692

order1152
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C3×D3×#127

Splittings

FittingC2×C32×#127 ⋊ C2
SylowC32 ⋊ C22×#127

Subgroups

subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#127C2
socleC23×C32C24
hypercenterC2×C3×#127D3
hypocenterC3C22×C3×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#127

6249 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D32×#127, C3×D3×#3151, D3×#83163, …
maximal normal subgroup ofC2×D32×#127, C3×D3×#3151, D3×#83163, …
maximal quotient ofC3×D3×#3151, D3×#127×AGL(1,𝔽7), C2×#127×AGL(1,ℤ/9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 134703);