C₅₉×#21683 #28433792

order	15104
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅₉×#21683

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₅₉	C₂³
commutator	C₂³	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₂³×C₄
prime radical	C₅₉×#2397	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₅₉ ◁ G

1266 conjugacy classes of subgroups; only the 406 normal subgroups are shown.

normal subgroups only

This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 406 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 4 generators on 83 points:

(2,4)(6,8)(9,10,13,17,14,12,16,21)(11,15,20,23,18,19,22,24)(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);(1,2,3,4)(9,11)(10,15)(12,19)(13,20)(14,18)(16,22)(17,23)(21,24);(5,6,7,8)(11,18)(15,19)(20,22)(23,24);(9,12,13,21,14,10,16,17)(11,19,20,24,18,15,22,23)

Conjugacy classes & character table

5192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 14671);