C₅₉×#7238 #28419347

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

Aliases

direct product

C₅₉×#7238

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#342
commutator	C₂²×C₄	C₄²×C₅₉
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₅₉
prime radical	C₂³×C₅₉	#95
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 2 generators on 83 points:

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

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, 226);