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C3×D5291 #44540799

order31746
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5291
unambiguous semidirect productC11⋊(C3×D481)

Splittings

Fitting, socle, HallC3×C11×C13×C37 ⋊ C2
derived, HallC11×C13×C37 ⋊ C2×C3
HallC3×C13×C37 ⋊ D11
HallC3×C11×C37 ⋊ D13
HallC13×C37 ⋊ C3×D11
HallC3×C11×C13 ⋊ D37
HallC11×C37 ⋊ C3×D13
HallC11×C13 ⋊ C3×D37
HallC3×C37 ⋊ D143
HallC3×C13 ⋊ D407
SylowC37 ⋊ C3×D143
HallC3×C11 ⋊ D481
SylowC13 ⋊ C3×D407
SylowC11 ⋊ C3×D481

Subgroups

subgroupG/H
center, hypercenterC3D5291
commutator, cosocle, hypocenterC11×C13×C37C2×C3
FrattiniC1G
Fitting, socleC3×C11×C13×C37C2
LCSG ▷ C11×C13×C37
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 15873

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

Conjugacy classes & character table

7941 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 12);