C₅₉×#12769 #28424878

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12767
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅₉×#12769

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#1790
commutator	C₂×D₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×#41	C₂³×C₅₉
prime radical	C₅₉×#3549	C₂
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×#41×C₅₉ ◁ G

856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 75
transitive degree	μ_t(G) = 944

A minimal faithful permutation representation — 3 generators on 75 points:

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

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, 5757);