C₅₉×#12314 #28424423

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12314
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#12314

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ G

384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 75
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 3 generators on 75 points:

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

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5302);