#49089878

order	35868
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇²×C₆₁ ⋊ C₂²×C₃
Hall	D₇×D₄₂₇ ⋊ C₃
Hall	#22582225 ⋊ C₂²
Sylow	C₆₁ ⋊ #64423⋊C₂
Sylow	C₇² ⋊ C₂×D₆₁⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₆₁	C₂²×C₃
LCS	G ▷ C₇²×C₆₁
UCS	C₁

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 854

A minimal faithful permutation representation — 2 generators on 75 points:

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

Polycyclic presentation:

2^2,3,7^2,61|e^a=e^6,f^a=f^60,d^b=d^6,d^c=d^2,e^c=e^2,f^c=f^47

Conjugacy classes & character table

369 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35868, 230);