C₇₃×#20019 #32929423

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₇₃×#20019

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄²×C₇₃ ◁ G

598 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 9344

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

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

Conjugacy classes & character table

3577 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 13007);