C₇₃×#9478 #32918882

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₃×#9478

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₇₃
Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₂⁴×C₇₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

610 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 97
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 3 generators on 97 points:

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

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, 2466);