C₂³×C₄×C₈×C₅₉ #28472159

order	15104
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian

C₂³×C₄×C₈×C₅₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
socle, prime radical	C₂⁵×C₅₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

4638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 5 generators on 77 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂³×C₄×C₁₆×C₅₉, C₂³×C₈²×C₅₉, C₂²×C₄²×C₈×C₅₉, …
maximal normal subgroup of	C₂³×C₄×C₁₆×C₅₉, C₂³×C₈²×C₅₉, C₂²×C₄²×C₈×C₅₉, …
maximal quotient of	C₂³×C₄×C₁₆×C₅₉, C₂³×C₈²×C₅₉, C₂²×C₄²×C₈×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 53038);

C23×C4×C8×C59 #28472159