C₇₃×#7145 #32916549

order	18688
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₇₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₇₃×#7145

Subgroups

	subgroup	G/H
center	C₄²×C₇₃	C₄²
commutator	C₄	C₄×C₁₆×C₇₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₇₃
socle	C₂²×C₇₃	#336
prime radical	C₂³×C₇₃	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄²×C₇₃ ◁ G

222 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 9344

A minimal faithful permutation representation — 2 generators on 105 points:

(1,2)(3,10,12,16)(4,8)(5,14)(6,9)(7,11,15,13)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,5,13,6,12,4,11)(2,7,8,10,9,15,14,16)

Conjugacy classes & character table

6424 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 133);