C₅₉×#12082 #28424191

order	15104
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅₉×#12082

Subgroups

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₅₉
Frattini, cosocle	C₄×C₈	C₂³×C₅₉
socle	C₂²×C₅₉	C₄×D₈
prime radical	C₂×D₈×C₅₉	C₂×C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₄×C₈×C₅₉ ◁ C₈²×C₅₉ ◁ G

224 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 83
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

4484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5070);