C₅₉×#7605 #28419714

order	15104
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#7605

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

440 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 154 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) = 91
transitive degree	μ_t(G) = 15104

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,3,6,4,5,7,8)(9,10,12,15,13,16,11,14)(17,18)(19,25)(20,28)(21,23)(22,26)(24,30)(27,32)(29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(2,5)(3,7)(17,19,21,27)(18,22,23,31)(20,29,30,26)(24,32,28,25);(9,11,13,12)(10,14,16,15)(18,23)(22,31)(24,28)(25,32)

Conjugacy classes & character table

3068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 593);