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C5⋊((C13⋊C3)⋊D73) #43249727

order28470
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊((C13⋊C3)⋊D73)
unambiguous semidirect product(C13⋊C3)⋊D365

Splittings

Fitting, socle, derived, HallC5×C13×C73 ⋊ C2×C3
HallC5×C13⋊C3×C73 ⋊ C2
HallD4745 ⋊ C3
HallC13⋊C3×C73 ⋊ D5
HallC13×C73 ⋊ C3×D5
HallC5×C73 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ D73
SylowC73 ⋊ C5⋊(D13⋊C3)
HallC5×C13 ⋊ C3×D73
HallC13⋊C3 ⋊ D365
SylowC13 ⋊ C3×D365
SylowC5 ⋊ (C13⋊C3)⋊D73

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C73C2×C3
LCSG ▷ C5×C13×C73
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 91
transitive degreeμt(G) = 4745

A minimal faithful permutation representation — 2 generators on 91 points:

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

Polycyclic presentation:

2,3,5,13,73|c^a=c^4,d^a=d^12,e^a=e^72,d^b=d^3

Conjugacy classes & character table

1282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28470, 46);