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C5×D2847 #43249697

order28470
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2847
unambiguous semidirect productC3⋊(C5×D949)
unambiguous semidirect productC13⋊(C5×D219)
unambiguous semidirect productC73⋊(C5×D39)

Splittings

Fitting, socle, HallC3×C5×C13×C73 ⋊ C2
derived, HallC3×C13×C73 ⋊ C2×C5
HallC5×C13×C73 ⋊ D3
HallC3×C5×C73 ⋊ D13
HallC13×C73 ⋊ C5×D3
HallC5×C73 ⋊ D39
HallC3×C73 ⋊ C5×D13
HallC3×C5×C13 ⋊ D73
SylowC73 ⋊ C5×D39
HallC5×C13 ⋊ D219
HallC3×C13 ⋊ C5×D73
HallC3×C5 ⋊ D949
SylowC13 ⋊ C5×D219
SylowC3 ⋊ C5×D949

Subgroups

subgroupG/H
center, hypercenterC5D2847
commutator, cosocle, hypocenterC3×C13×C73C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C73C2
LCSG ▷ C3×C13×C73
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 94
transitive degreeμt(G) = 14235

A minimal faithful permutation representation — 2 generators on 94 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);(7,8)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,94)(24,93)(25,92)(26,91)(27,90)(28,89)(29,88)(30,87)(31,86)(32,85)(33,84)(34,83)(35,82)(36,81)(37,80)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Conjugacy classes & character table

7125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28470, 16);