C₄×C₈²×C₅₉ #28419947

order	15104
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄²×C₈

Aliases

abelian

C₄×C₈²×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
socle, prime radical	C₂³×C₅₉	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 15104

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

(1,2,3,4,5,6,7,8)(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);(9,10,11,12,13,14,15,16);(17,18,19,20)

Conjugacy classes & character table

15104 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₈×C₁₆×C₅₉, C₈³×C₅₉, C₂×C₄×C₈²×C₅₉
maximal normal subgroup of	C₄×C₈×C₁₆×C₅₉, C₈³×C₅₉, C₂×C₄×C₈²×C₅₉
maximal quotient of	C₄×C₈×C₁₆×C₅₉, C₈³×C₅₉, C₂×C₄×C₈²×C₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 826);

C4×C82×C59 #28419947