C₅₉×#12324 #28424433

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#12324

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₅₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄²×C₅₉ ◁ C₅₉×#436 ◁ G

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

normal subgroups only

This group has 406 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) = 83
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

1829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5312);