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C3×D3965 #37558172

order23790
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3965
unambiguous semidirect productC5⋊(C3×D793)

Splittings

Fitting, socle, HallC3×C5×C13×C61 ⋊ C2
derived, HallC5×C13×C61 ⋊ C2×C3
HallC3×C13×C61 ⋊ D5
HallC3×C5×C61 ⋊ D13
HallC13×C61 ⋊ C3×D5
HallC5×C61 ⋊ C3×D13
HallC3×C5×C13 ⋊ D61
HallC3×C61 ⋊ D65
HallC5×C13 ⋊ C3×D61
SylowC61 ⋊ C3×D65
HallC3×C13 ⋊ D305
HallC3×C5 ⋊ D793
SylowC13 ⋊ C3×D305
SylowC5 ⋊ C3×D793

Subgroups

subgroupG/H
center, hypercenterC3D3965
commutator, cosocle, hypocenterC5×C13×C61C2×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C61C2
LCSG ▷ C5×C13×C61
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 82
transitive degreeμt(G) = 11895

A minimal faithful permutation representation — 2 generators on 82 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);(5,8)(6,7)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,82)(24,81)(25,80)(26,79)(27,78)(28,77)(29,76)(30,75)(31,74)(32,73)(33,72)(34,71)(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

5952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 17);