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C3×D5635 #46798905

order33810
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5635
unambiguous semidirect productC5⋊(C3×D1127)
unambiguous semidirect productC23⋊(C3×D245)

Splittings

Fitting, HallC3×C5×C23×C49 ⋊ C2
derived, HallC5×C23×C49 ⋊ C2×C3
HallC3×C23×C49 ⋊ D5
HallC23×C49 ⋊ C3×D5
HallC3×C5×C49 ⋊ D23
HallC3×C5×C23 ⋊ D49
HallC5×C49 ⋊ C3×D23
HallC3×C49 ⋊ D115
HallC5×C23 ⋊ C3×D49
HallC3×C23 ⋊ D245
SylowC49 ⋊ C3×D115
SylowC23 ⋊ C3×D245
HallC3×C5 ⋊ D1127
SylowC5 ⋊ C3×D1127

Subgroups

subgroupG/H
center, hypercenterC3D5635
commutator, cosocle, hypocenterC5×C23×C49C2×C3
FrattiniC7C3×D805
FittingC3×C5×C23×C49C2
socleC3×C5×C7×C23D7
LCSG ▷ C5×C23×C49
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 80
transitive degreeμt(G) = 16905

A minimal faithful permutation representation — 2 generators on 80 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);(5,8)(6,7)(10,57)(11,56)(12,55)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

8457 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 9);