C₅₉×#7213 #28419322

order	15104
nilpotency class	4
isoclinism	isoclinic class of #7213
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#7213

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#342
commutator	C₂²×C₄	C₄²×C₅₉
Frattini, cosocle	C₂²×C₂²⋊C₄	C₂²×C₅₉
prime radical	C₂⁵×C₅₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂⁴×C₅₉ ◁ C₂²×C₂²⋊C₄×C₅₉ ◁ G

560 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 82 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 — 2 generators on 75 points:

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

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 201);