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Cayley diagram

C22⋊C4×D9 #63442

order288
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D9

Splittings

FittingC9×C22⋊C4 ⋊ C2
SylowC9 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC22C22×D9
commutatorC2×C9C22×C4
Frattini, socleC22×C3C22×D3
FittingC9×C22⋊C4C2
prime radicalC23×D9C2
cosocleC22×C9C23
hypercenterC22⋊C4D9
hypocenterC9C2×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22⋊C4

198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 72

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

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×#99, C2×C22⋊C4×D9, #10589588, …
maximal normal subgroup ofD9×#99, C2×C22⋊C4×D9, #10589588, …
maximal quotient of#10588326, D9×#95, #10588344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 90);