C₇₃×#13341 #32922745

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

Aliases

direct product

C₇₃×#13341

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#97×C₇₃ ◁ G

594 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 93
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 3 generators on 93 points:

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

Conjugacy classes & character table

2482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6329);