C₅₉×#7521 #28419630

order	15104
nilpotency class	6
isoclinism	isoclinic class of #7519
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#7521

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1402
commutator	C₄⋊Q₈	C₂×C₄×C₅₉
Frattini, cosocle	#494	C₂²×C₅₉
prime radical	C₅₉×#555	C₄
LCS	G ▷ C₄⋊Q₈ ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₄²×C₅₉ ◁ C₅₉×#494 ◁ G

148 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 30 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:

(1,2,4,9,5,11,17,29)(3,12,14,26,13,23,32,27)(6,10,21,30,19,31,18,28)(7,16,22,20,8,24,25,15)(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);(2,7)(3,13)(8,11)(9,26)(10,12)(14,32)(15,20)(16,24)(22,28)(23,31)(25,30)(27,29)

Conjugacy classes & character table

1298 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 509);