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C3×D5551 #45686554

order33306
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5551

Splittings

Fitting, socle, HallC3×C7×C13×C61 ⋊ C2
derived, HallC7×C13×C61 ⋊ C2×C3
HallC3×C13×C61 ⋊ D7
HallC3×C7×C61 ⋊ D13
HallC13×C61 ⋊ C3×D7
HallC7×C61 ⋊ C3×D13
HallC3×C7×C13 ⋊ D61
HallC3×C61 ⋊ D91
HallC7×C13 ⋊ C3×D61
SylowC61 ⋊ C3×D91
HallC3×C13 ⋊ D427
HallC3×C7 ⋊ D793
SylowC13 ⋊ C3×D427
SylowC7 ⋊ C3×D793

Subgroups

subgroupG/H
center, hypercenterC3D5551
commutator, cosocle, hypocenterC7×C13×C61C2×C3
FrattiniC1G
Fitting, socleC3×C7×C13×C61C2
LCSG ▷ C7×C13×C61
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 84
transitive degreeμt(G) = 16653

A minimal faithful permutation representation — 2 generators on 84 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);(5,10)(6,9)(7,8)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(25,84)(26,83)(27,82)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)

Conjugacy classes & character table

8331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33306, 21);