#27190183

order	13140
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

derived, Hall	C₅×C₇₃ ⋊ C₄×C₉
Hall	C₅×#10620321 ⋊ C₄
Hall	#13091734 ⋊ C₉
Hall	#10620321 ⋊ AGL(1,𝔽₅)
Sylow	C₇₃ ⋊ C₉×AGL(1,𝔽₅)
Sylow	C₅ ⋊ #14581466

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	#13091734⋊C₃
commutator, hypocenter	C₅×C₇₃	C₄×C₉
Fitting, socle	C₃×C₅×C₇₃	C₃×C₄
prime radical, cosocle	C₃×D₅×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₇₃
UCS	C₁ ◁ C₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 3285

A minimal faithful permutation representation — 2 generators on 87 points:

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

Polycyclic presentation:

2,3,2,5,73,3|a^2=c,b^3=f,d^a=d^2,e^a=e^72,e^b=e^8,d^c=d^4

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13140, 17);