Finite Group Databasebeta

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Cayley diagram

C3×#829 #63615

order288
isoclinismisoclinic class of #826
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×#829

Splittings

SylowC32 ⋊ Q32

Subgroups

subgroupG/H
centerC2×C3#213
commutator, cosocleC3×C8C22×C3
FrattiniC8C2×C3×D3
FittingC32×Q16C2
socle, prime radicalC2×C32D8
hypercenterC3×Q16D3
hypocenterC3C3×Q32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×Q16

57 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 96

A minimal faithful permutation representation — 2 generators on 38 points:

(1,2,3)(4,5,6)(7,20,12,9)(8,30,16,13)(10,38,25,22)(11,19,23,27)(14,37,33,32)(15,29,26,34)(17,21,36,35)(18,24,28,31);(5,6)(7,16,12,8)(9,36,20,17)(10,35,25,21)(11,15,23,26)(13,18,30,28)(14,24,33,31)(19,32,27,37)(22,29,38,34)

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#829, #10591042, #10591043, …
maximal normal subgroup ofD3×#829, #10591042, #10591043, …
maximal quotient ofC3×#4489, C3×#4492, C3×#4564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 263);