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C3×D5467 #45659018

order32802
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5467
unambiguous semidirect productC11⋊(C3×D497)
unambiguous semidirect productC71⋊(C3×D77)

Splittings

Fitting, socle, HallC3×C7×C11×C71 ⋊ C2
derived, HallC7×C11×C71 ⋊ C2×C3
HallC3×C11×C71 ⋊ D7
HallC3×C7×C71 ⋊ D11
HallC11×C71 ⋊ C3×D7
HallC7×C71 ⋊ C3×D11
HallC3×C7×C11 ⋊ D71
HallC3×C71 ⋊ D77
HallC7×C11 ⋊ C3×D71
SylowC71 ⋊ C3×D77
HallC3×C11 ⋊ D497
HallC3×C7 ⋊ D781
SylowC11 ⋊ C3×D497
SylowC7 ⋊ C3×D781

Subgroups

subgroupG/H
center, hypercenterC3D5467
commutator, cosocle, hypocenterC7×C11×C71C2×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C71C2
LCSG ▷ C7×C11×C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 92
transitive degreeμt(G) = 16401

A minimal faithful permutation representation — 2 generators on 92 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92);(5,10)(6,9)(7,8)(12,21)(13,20)(14,19)(15,18)(16,17)(23,92)(24,91)(25,90)(26,89)(27,88)(28,87)(29,86)(30,85)(31,84)(32,83)(33,82)(34,81)(35,80)(36,79)(37,78)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Conjugacy classes & character table

8205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 10);