C₅₉×#12231 #28424340

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12093
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#12231

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₅₉
prime radical	C₅₉×#392	C₂²
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₅₉ ◁ C₂×C₂²⋊C₄×C₅₉ ◁ G

412 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 70 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)(3,8,15,24)(4,7,16,9)(6,11,13,22)(12,25,27,32)(14,19,30,23)(17,21,29,31)(18,20,28,26)(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)(3,12)(4,16)(8,21)(9,10)(11,20)(14,29)(15,27)(17,30)(18,28)(19,25)(22,26)(23,32)(24,31);(1,3,13,27)(2,8,22,32)(4,17,28,30)(5,15,6,12)(7,19,26,31)(9,23,20,21)(10,24,11,25)(14,16,29,18)

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5219);