C₇₃×#10508 #32919912

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

Aliases

direct product

C₇₃×#10508

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	C₇₃×#3213	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

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

normal subgroups only

This group has 414 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) = 97
transitive degree	μ_t(G) = 4672

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

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

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, 3496);