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C5×D2667 #40998684

order26670
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2667
unambiguous semidirect productC3⋊(C5×D889)
unambiguous semidirect productC7⋊(C5×D381)
unambiguous semidirect productC127⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C127 ⋊ C2
derived, HallC3×C7×C127 ⋊ C2×C5
HallC5×C7×C127 ⋊ D3
HallC3×C5×C127 ⋊ D7
HallC7×C127 ⋊ C5×D3
HallC5×C127 ⋊ D21
HallC3×C127 ⋊ C5×D7
SylowC127 ⋊ C5×D21
HallC3×C5×C7 ⋊ D127
HallC5×C7 ⋊ D381
HallC3×C7 ⋊ C5×D127
HallC3×C5 ⋊ D889
SylowC7 ⋊ C5×D381
SylowC3 ⋊ C5×D889

Subgroups

subgroupG/H
center, hypercenterC5D2667
commutator, cosocle, hypocenterC3×C7×C127C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C127C2
LCSG ▷ C3×C7×C127
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 142
transitive degreeμt(G) = 13335

A minimal faithful permutation representation — 2 generators on 142 points:

(1,2,3,4,5)(6,7,8)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142);(7,8)(10,15)(11,14)(12,13)(17,142)(18,141)(19,140)(20,139)(21,138)(22,137)(23,136)(24,135)(25,134)(26,133)(27,132)(28,131)(29,130)(30,129)(31,128)(32,127)(33,126)(34,125)(35,124)(36,123)(37,122)(38,121)(39,120)(40,119)(41,118)(42,117)(43,116)(44,115)(45,114)(46,113)(47,112)(48,111)(49,110)(50,109)(51,108)(52,107)(53,106)(54,105)(55,104)(56,103)(57,102)(58,101)(59,100)(60,99)(61,98)(62,97)(63,96)(64,95)(65,94)(66,93)(67,92)(68,91)(69,90)(70,89)(71,88)(72,87)(73,86)(74,85)(75,84)(76,83)(77,82)(78,81)(79,80)

Conjugacy classes & character table

6675 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 18);