C₂×C₅₉×#1411 #28425697

order	15104
nilpotency class	5
isoclinism	isoclinic class of #1408
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂×C₅₉×#1411

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#353
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	C₄⋊Q₈	C₂³×C₅₉
prime radical	C₂³×C₅₉	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄⋊Q₈×C₅₉ ◁ G

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

normal subgroups only

This group has 398 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) = 93
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 93 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,4,6,11,8,13,20,30)(5,14,15,28,17,25,32,33)(7,12,22,29,23,10,19,27)(9,18,24,21,26,31,34,16);(3,5,8,17)(4,9,13,26)(6,18,20,31)(7,21,23,16)(10,25,12,14)(11,28,30,33)(15,19,32,22)(24,29,34,27)

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6576);