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Cayley diagram

C3×Dic24 #63587

order288
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic24

Splittings

SylowC32 ⋊ Q32

Subgroups

subgroupG/H
centerC2×C3D24
commutator, cosocleC3×C8C22×C3
FrattiniC8C2×C3×D3
FittingC32×C16C2
socle, prime radicalC2×C32D8
hypercenterC3×C16D3
hypocenterC3C3×Q32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×C16

53 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)(7,34,24,21,23,19,18,20,12,38,10,9,11,26,29,35)(8,32,30,28,25,17,22,27,16,36,14,13,15,33,37,31);(5,6)(7,16,12,8)(9,33,21,17)(10,37,24,22)(11,15,23,25)(13,19,28,26)(14,18,30,29)(20,32,35,36)(27,38,31,34)

Conjugacy classes & character table

81 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10589072, #10589074, #10589075, …
maximal normal subgroup of#10589072, #10589074, #10589075, …
maximal quotient ofC3×#4503, C3×#4504, C2×C3×Dic24, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 235);