#49089741

order	35868
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

derived, Hall	C₇²×C₆₁ ⋊ C₃×C₄
Hall	C₆₁×C₇⋊Dic₇ ⋊ C₃
Hall	#22582226 ⋊ C₄
Hall	C₇⋊Dic₇ ⋊ C₆₁⋊C₃
Sylow	C₆₁ ⋊ #10596874
Sylow	C₇² ⋊ C₄×C₆₁⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#31822441
commutator, hypocenter	C₇²×C₆₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₆₁	C₂×C₃
prime radical	C₂×#22582226	C₂
LCS	G ▷ C₇²×C₆₁
UCS	C₁ ◁ C₂

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 11956

A minimal faithful permutation representation — 3 generators on 79 points:

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

Polycyclic presentation:

2,3,7^2,61,2|a^2=f,c^a=c^6,d^a=d^6,c^b=c^2,d^b=d^2,e^b=e^13

Conjugacy classes & character table

1068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35868, 93);