#49089877

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	#22582226 ⋊ 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)(23,39,55)(24,40,37)(25,43,29)(28,52,34)(31,56,62)(32,57,51)(33,61,42)(35,53,36)(41,71,47)(44,64,60)(45,63,67)(48,70,59)(49,54,72)(50,58,68)(65,69,73)(66,74,75);(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)(35,47)(37,49)(39,50)(42,55)(43,58)(45,60)(46,62)(48,64)(51,65)(52,59)(53,57)(54,69)(56,66)(61,73)(63,72)(67,71)(68,75)(70,74)

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^13

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, 229);