C₅₉×#12273 #28424382

order	15104
nilpotency class	4
isoclinism	isoclinic class of #12152
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#12273

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₅₉
prime radical	C₂³×C₅₉	#120
LCS	G ▷ C₂×C₄⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₅₉ ◁ C₂×C₄⋊C₄×C₅₉ ◁ G

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

normal subgroups only

This group has 364 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) = 3776

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

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

Conjugacy classes & character table

1829 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 5261);