C₅₉×#33564 #28445673

order	15104
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₅₉×#33564

Subgroups

	subgroup	G/H
center	C₄×C₅₉	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₅₉
socle	C₂×C₅₉	C₂×B(4,𝔽₂)
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂×C₄×C₅₉ ◁ C₂×#41×C₅₉ ◁ G

1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 218 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 — 4 generators on 91 points:

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

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, 26552);