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C4×#64091 #11801984

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productC4×#64091

Splittings

FittingC32×C4×C22⋊C4 ⋊ C2
SylowC32 ⋊ C4×#120

Subgroups

subgroupG/H
centerC22×C4C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC32×C4×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC2×#64091C2
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

3672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C3⋊D3×#120, AGL(1,𝔽5)×#64091, C4×#10590410
maximal normal subgroup ofC4×C3⋊D3×#120, C4×#10590410
maximal quotient ofAGL(1,𝔽5)×#64091

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 35995);