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C3×#88324 #11929656

order1272
isoclinismisoclinic class of #6157
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×#88324

Splittings

derived, SylowC53 ⋊ C3×C8
HallC3×C53 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC2×C3#6157
commutator, hypocenterC53C3×C8
FrattiniC2C3×#6157
Fitting, socle, prime radicalC2×C3×C53C4
cosocleDic53C2×C3
LCSG ▷ C53
UCSC1 ◁ C2×C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 1272

A minimal faithful permutation representation — 2 generators on 64 points:

(1,2,3)(5,6,7,9)(8,11,12,18)(10,15,16,14)(13,20,21,31)(17,24,25,27)(19,28,29,23)(22,33,34,46)(26,37,38,43)(30,35,41,40)(32,44,45,36)(39,47,48,53)(42,49,50,52)(51,54,55,56)(57,58,59,61,60,62,63,64);(4,5,8,13,22,35,24,11,19,30,42,51,54,47,33,45,31,43,52,48,38,25,16,9,14,23,36,44,28,15,6,10,17,26,39,49,37,20,32,46,53,56,55,50,41,29,18,27,40,34,21,12,7)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1272, 5);