#72209608

order	4860
isoclinism	isoclinic class of #72209608
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

Splittings

Fitting, socle

C₃⁴ ⋊ A₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₃⁴	A₅
LCS	G
UCS	C₁

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,2)(3,8)(4,7)(6,11)(12,14)(13,15);(2,5,6)(7,10,13)(8,9,12);(1,3,4)(2,7,8)(5,9,10)(6,12,13)(11,14,15);(1,3,4)(2,8,7)(5,10,9)(6,12,13)(11,14,15);(1,3,4)(2,8,7)(5,9,10)(6,13,12)(11,14,15);(1,4,3)(2,8,7)(5,9,10)(6,12,13)(11,14,15)

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72209958
maximal quotient of	#72209635, #72209678

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,2)(3,8)(4,7)(6,11)(12,14)(13,15), (2,5,6)(7,10,13)(8,9,12), (1,3,4)(2,7,8)(5,9,10)(6,12,13)(11,14,15), (1,3,4)(2,8,7)(5,10,9)(6,12,13)(11,14,15), (1,3,4)(2,8,7)(5,9,10)(6,13,12)(11,14,15), (1,4,3)(2,8,7)(5,9,10)(6,12,13)(11,14,15));