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Cayley diagram

C4×C9⋊A4 #88679

order432
isoclinismisoclinic class of C9⋊A4
automorphismAut(G) = C2×C3×D3×A4 (order 432) · Inn(G) = C3×A4 · Out(G) = C22×C3
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×C9⋊A4
unambiguous semidirect product(C4×C9)⋊A4

Splittings

FittingC22×C4×C9 ⋊ C3
SylowC22×C4 ⋊ 3−1+2

Subgroups

subgroupG/H
centerC3×C4C3×A4
commutatorC22×C3C32×C4
FrattiniC2×C3C2×C3×A4
FittingC22×C4×C9C3
socle, cosocleC23×C3C2×C32
prime radicalC2×C3×A4C2×C3
hypercenterC4×C9A4
hypocenterC22C4×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C3×C4 ◁ C4×C9

69 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 108

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2,3,4)(5,8)(6,7)(9,15,16,11,10,17,14,12,13);(6,7,8)(10,12,15)(13,17,16)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C9⋊C8)⋊A4, C8×C9⋊A4, Dic18⋊A4, …
maximal normal subgroup of(C9⋊C8)⋊A4, C8×C9⋊A4, Dic18⋊A4, …
maximal quotient ofC4×C9⋊SL(2,𝔽3), C8×C9⋊A4, #11721339, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 326);