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C3×D5957 #49088349

order35742
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5957
unambiguous semidirect productC23⋊(C3×D259)

Splittings

Fitting, socle, HallC3×C7×C23×C37 ⋊ C2
derived, HallC7×C23×C37 ⋊ C2×C3
HallC3×C23×C37 ⋊ D7
HallC23×C37 ⋊ C3×D7
HallC3×C7×C37 ⋊ D23
HallC3×C7×C23 ⋊ D37
HallC7×C37 ⋊ C3×D23
HallC7×C23 ⋊ C3×D37
HallC3×C37 ⋊ D161
HallC3×C23 ⋊ D259
SylowC37 ⋊ C3×D161
SylowC23 ⋊ C3×D259
HallC3×C7 ⋊ D851
SylowC7 ⋊ C3×D851

Subgroups

subgroupG/H
center, hypercenterC3D5957
commutator, cosocle, hypocenterC7×C23×C37C2×C3
FrattiniC1G
Fitting, socleC3×C7×C23×C37C2
LCSG ▷ C7×C23×C37
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 70
transitive degreeμt(G) = 17871

A minimal faithful permutation representation — 2 generators on 70 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);(5,10)(6,9)(7,8)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(35,70)(36,69)(37,68)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

8940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 12);