C₅₉×#12898 #28425007

order	15104
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#12898

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₅₉	C₂³
commutator	C₂²	C₂²×C₁₆×C₅₉
Frattini, cosocle	C₂²×C₈	C₂³×C₅₉
socle, prime radical	C₂³×C₅₉	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₅₉ ◁ G

414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 286 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) = 15104

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

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

Conjugacy classes & character table

6608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5886);