A₅×C₇₉ #18011641

order	4740
isoclinism	isoclinic class of A₅
automorphism	?
homology	Abelianization (H₁) = C₇₉ · Schur multiplier (H₂) = C₂

non-solvable

Aliases

direct product

A₅×C₇₉

Subgroups

	subgroup	G/H
center, Fitting, hypercenter	C₇₉	A₅
commutator, hypocenter	A₅	C₇₉
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₇₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 395

A minimal faithful permutation representation — 2 generators on 84 points:

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

Conjugacy classes & character table

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

Relationships

derived subgroup of	A₅×C₇₉⋊C₃
socle of	A₅×C₇₉⋊C₃
maximal subgroup of	C₃×A₅×C₇₉, A₅×C₇₉⋊C₃, C₅×A₅×C₇₉, …
maximal normal subgroup of	C₃×A₅×C₇₉, A₅×C₇₉⋊C₃, C₅×A₅×C₇₉, …
maximal quotient of	C₃×A₅×C₇₉, C₅×A₅×C₇₉, C₇×A₅×C₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4740, 41);

A5×C79 #18011641