C₅₉×#7495 #28419604

order	15104
nilpotency class	5
isoclinism	isoclinic class of #7493
automorphism	?
homology	Abelianization (H₁) = C₄²×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#7495

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1390
commutator	C₂×D₄	C₄²×C₅₉
Frattini, cosocle	C₂×#124	C₂²×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂×C₄
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#124×C₅₉ ◁ G

280 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 91
transitive degree	μ_t(G) = 1888

A minimal faithful permutation representation — 2 generators on 91 points:

(1,2,4,9,6,10,18,29)(3,12,14,30,13,25,31,27)(5,11,21,28,20,8,17,26)(7,22,23,15,24,16,32,19)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3)(2,7,10,24)(4,16)(5,19)(6,13)(8,25,11,12)(9,27,29,30)(14,21)(15,20)(17,31)(18,22)(23,26,32,28)

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, 483);