C₅₉×#12803 #28424912

order	15104
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#12803

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂²×Q₈	C₂³×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

480 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 79
transitive degree	μ_t(G) = 3776

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

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

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5791);