C₅₉×#13432 #28425541

order	15104
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₅₉×#13432

Subgroups

	subgroup	G/H
center, socle	C₂×C₅₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₅₉
prime radical	C₅₉×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×#41×C₅₉ ◁ G

440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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)(3,12)(4,7)(5,18)(6,11)(8,15)(9,16)(10,19)(13,26)(14,29)(17,24)(20,30)(21,31)(22,32)(23,28)(25,27)(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);(2,7)(3,13)(4,16)(8,20)(9,11)(10,21)(12,25)(17,31)(18,24)(22,23)(26,29)(30,32);(1,3,4,14,6,13,16,27)(2,8,9,22,11,23,7,20)(5,15,17,30,19,28,31,32)(10,12,24,25,18,26,21,29)

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 6420);