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C5×D2937 #44440329

order29370
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2937
unambiguous semidirect productC3⋊(C5×D979)
unambiguous semidirect productC89⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C89 ⋊ C2
derived, HallC3×C11×C89 ⋊ C2×C5
HallC5×C11×C89 ⋊ D3
HallC3×C5×C89 ⋊ D11
HallC11×C89 ⋊ C5×D3
HallC5×C89 ⋊ D33
HallC3×C89 ⋊ C5×D11
HallC3×C5×C11 ⋊ D89
SylowC89 ⋊ C5×D33
HallC5×C11 ⋊ D267
HallC3×C11 ⋊ C5×D89
HallC3×C5 ⋊ D979
SylowC11 ⋊ C5×D267
SylowC3 ⋊ C5×D979

Subgroups

subgroupG/H
center, hypercenterC5D2937
commutator, cosocle, hypocenterC3×C11×C89C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C89C2
LCSG ▷ C3×C11×C89
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 108
transitive degreeμt(G) = 14685

A minimal faithful permutation representation — 2 generators on 108 points:

(1,2,3,4,5)(6,7,8)(9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108);(7,8)(10,19)(11,18)(12,17)(13,16)(14,15)(21,108)(22,107)(23,106)(24,105)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29370, 14);