C₅₉×#13217 #28425326

order	15104
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#13217

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₅₉
Frattini, cosocle	C₂²×D₄	C₂³×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 79
transitive degree	μ_t(G) = 3776

A minimal faithful permutation representation — 3 generators on 79 points:

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

Conjugacy classes & character table

2183 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6205);