C₇₃×#19096 #32928500

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₃×#19096

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

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

normal subgroups only

This group has 906 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) = 105
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 4 generators on 105 points:

(2,7)(3,10)(4,5)(9,12)(11,13)(14,16)(18,23)(20,21)(24,31)(25,26)(27,29)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,2,6,9)(3,8,11,15)(4,12,5,7)(10,16,13,14)(17,18,22,26)(19,24,28,32)(20,23,21,25)(27,30,29,31);(1,3)(2,8)(4,10)(5,13)(6,11)(7,14)(9,15)(12,16)(17,19)(18,24)(20,27)(21,29)(22,28)(23,30)(25,31)(26,32);(2,9)(7,12)(8,15)(14,16)(17,20,22,21)(18,25,26,23)(19,27,28,29)(24,31,32,30)

Conjugacy classes & character table

2263 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 12084);