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C5×D3201 #44544965

order32010
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3201
unambiguous semidirect productC3⋊(C5×D1067)
unambiguous semidirect productC97⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C97 ⋊ C2
derived, HallC3×C11×C97 ⋊ C2×C5
HallC5×C11×C97 ⋊ D3
HallC3×C5×C97 ⋊ D11
HallC11×C97 ⋊ C5×D3
HallC5×C97 ⋊ D33
HallC3×C97 ⋊ C5×D11
HallC3×C5×C11 ⋊ D97
SylowC97 ⋊ C5×D33
HallC5×C11 ⋊ D291
HallC3×C11 ⋊ C5×D97
HallC3×C5 ⋊ D1067
SylowC11 ⋊ C5×D291
SylowC3 ⋊ C5×D1067

Subgroups

subgroupG/H
center, hypercenterC5D3201
commutator, cosocle, hypocenterC3×C11×C97C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C97C2
LCSG ▷ C3×C11×C97
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 116
transitive degreeμt(G) = 16005

A minimal faithful permutation representation — 2 generators on 116 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);(7,8)(10,19)(11,18)(12,17)(13,16)(14,15)(21,116)(22,115)(23,114)(24,113)(25,112)(26,111)(27,110)(28,109)(29,108)(30,107)(31,106)(32,105)(33,104)(34,103)(35,102)(36,101)(37,100)(38,99)(39,98)(40,97)(41,96)(42,95)(43,94)(44,93)(45,92)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Conjugacy classes & character table

8010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 15);