C₇₃×#9970 #32919374

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

Aliases

direct product

C₇₃×#9970

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₃	#120
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₇₃×#2656	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

772 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 101
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 3 generators on 101 points:

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

Conjugacy classes & character table

2920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 2958);