C₅₉×#17338 #28429447

order	15104
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₅₉ · Schur multiplier (H₂) = C₂³×C₈

Aliases

direct product

C₅₉×#17338

Subgroups

	subgroup	G/H
center	C₄²×C₅₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂²×C₄²
prime radical	C₂⁴×C₅₉	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₅₉ ◁ G

712 conjugacy classes of subgroups; only the 518 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 518 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) = 3776

A minimal faithful permutation representation — 4 generators on 91 points:

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

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, 10326);