C₇₃×#13353 #32922757

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₃×#13353

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇₃
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

720 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 2336

A minimal faithful permutation representation — 3 generators on 105 points:

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

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6341);