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C3×#92535 #13093745

order1500
isoclinismisoclinic class of #92535
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productC3×#92535

Splittings

Fitting, HallC3×H(3,𝔽5) ⋊ C4
derived, SylowH(3,𝔽5) ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC3#92535
commutator, hypocenterH(3,𝔽5)C3×C4
FrattiniC5C3×#1042
FittingC3×H(3,𝔽5)C4
socleC3×C5#1042
prime radicalC3×(C5⋊D5)⋊C5C2
cosocle(C5⋊D5)⋊C5C2×C3
LCSG ▷ H(3,𝔽5)
UCSC1 ◁ C3

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 75

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3)(5,7)(6,11,12,22)(8,14)(9,17,10,20)(13,21,23,19)(15,25,26,28)(16,24,18,27);(4,5,18,24,23)(6,10,8,27,7)(9,15,25,17,12)(11,21,16,28,13)(14,20,22,19,26)

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(#1043⋊C5)⋊C2, C2×C3×#92535
maximal normal subgroup ofC3×(#1043⋊C5)⋊C2, C2×C3×#92535
maximal quotient ofC2×C3×#92535

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1500, 46);