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C3×D3913 #37553437

order23478
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3913

Splittings

Fitting, socle, HallC3×C7×C13×C43 ⋊ C2
derived, HallC7×C13×C43 ⋊ C2×C3
HallC3×C13×C43 ⋊ D7
HallC3×C7×C43 ⋊ D13
HallC13×C43 ⋊ C3×D7
HallC7×C43 ⋊ C3×D13
HallC3×C7×C13 ⋊ D43
HallC3×C43 ⋊ D91
HallC7×C13 ⋊ C3×D43
SylowC43 ⋊ C3×D91
HallC3×C13 ⋊ D301
HallC3×C7 ⋊ D559
SylowC13 ⋊ C3×D301
SylowC7 ⋊ C3×D559

Subgroups

subgroupG/H
center, hypercenterC3D3913
commutator, cosocle, hypocenterC7×C13×C43C2×C3
FrattiniC1G
Fitting, socleC3×C7×C13×C43C2
LCSG ▷ C7×C13×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 11739

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(5,10)(6,9)(7,8)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

5874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 26);