Finite Group Databasebeta

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Cayley diagram

C2×(C2×D9)⋊C4 #63489

order288
isoclinismisoclinic class of Dic18
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×(C2×D9)⋊C4

Splittings

FittingC22×C4×C9 ⋊ C2
SylowC9 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D9
commutatorC2×C9C22×C4
FrattiniC22×C3C22×D3
FittingC22×C4×C9C2
socleC23×C3C2×D3
prime radicalC23×D9C2
cosocleC22×C9C23
hypercenterC22×C4D9
hypocenterC9C2×C22⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4

198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 3 generators on 19 points:

(4,6)(7,8,9,10)(11,16,18,17,12,14,13,19,15);(3,4)(5,6)(12,14)(13,17)(15,16)(18,19);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10588146, #10588344, #10588345, …
maximal normal subgroup of#10588146, #10588344, #10588345, …
maximal quotient ofC2×#63364, #10588609, C4×(C2×D9)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 137);