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Cayley diagram

C9×C22⋊A4 #88904

order432
isoclinismisoclinic class of C22⋊A4
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C24×C3

Aliases

direct productC9×C22⋊A4

Splittings

FittingC24×C9 ⋊ C3
derived, SylowC24 ⋊ C3×C9

Subgroups

subgroupG/H
center, hypercenterC9C22⋊A4
commutator, hypocenterC24C3×C9
FrattiniC3C3×C22⋊A4
FittingC24×C9C3
socle, cosocleC24×C3C32
prime radicalC3×C22⋊A4C3
LCSG ▷ C24
UCSC1 ◁ C9

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 17 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC9⋊#1020, C9⋊#4625, #13146262, …
maximal subgroup of#11720761, C9×#120⋊C3, C9×#1020, …
maximal normal subgroup of#11720761, C9×#120⋊C3, C9×#1020, …
maximal quotient ofC9×C22⋊SL(2,𝔽3), C9×#997, C2×C9×C22⋊A4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 551);