C₅₉×#12688 #28424797

order	15104
nilpotency class	4
isoclinism	isoclinic class of #11499
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₅₉×#12688

Subgroups

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

1220 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 158 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:

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

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5676);