C₅₉×#13589 #28425698

order	15104
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₅₉×#13589

Subgroups

	subgroup	G/H
center	C₄×C₅₉	#353
commutator	C₄²	C₂²×C₄×C₅₉
Frattini, cosocle	C₄⋊Q₈	C₂³×C₅₉
socle	C₂×C₅₉	C₂×#353
prime radical	C₅₉×#3147	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₅₉×#532 ◁ G

408 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 1888

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

(1,2,5,10,6,11,21,28)(3,12,14,27,16,23,30,31)(4,8,17,25,18,9,20,26)(7,19,22,13,24,29,32,15)(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)(2,7)(4,13)(5,19)(6,16)(8,12)(9,23)(10,27)(11,24)(14,17)(15,18)(20,30)(21,29)(22,26)(25,32)(28,31);(1,4,6,18)(2,8,11,9)(3,13,16,15)(5,17,21,20)(7,12,24,23)(10,25,28,26)(14,29,30,19)(22,27,32,31)

Conjugacy classes & character table

2006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6577);