C₅₉×#12799 #28424908

order	15104
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₅₉×#12799

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂²×D₄	C₂³×C₅₉
prime radical	C₂×#127×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

588 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 1888

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

(2,4)(5,6)(7,10)(8,12,16,11)(9,13)(14,18)(15,17,20,19)(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);(1,2,3,4)(5,7)(6,10)(8,15)(9,14)(11,19)(12,17)(13,18)(16,20);(6,11)(7,14)(8,16)(10,17)(12,13)(18,19)

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, 5787);