C₇₃×#19058 #32928462

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₃×#19058

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	#532×C₇₃	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

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

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 121
transitive degree	μ_t(G) = 9344

A minimal faithful permutation representation — 4 generators on 121 points:

(1,2,5,8)(3,9,10,16)(4,12,13,7)(6,14,15,11)(17,18)(19,29)(20,34)(21,26)(22,27)(23,28)(24,32)(25,36)(30,38)(31,39)(33,42)(35,40)(37,41)(43,45)(44,47)(46,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(4,13)(7,12)(9,16)(11,14)(17,19)(18,24)(20,30)(21,31)(22,32)(23,33)(25,38)(26,29)(27,42)(28,39)(34,47)(35,44)(36,45)(37,46)(40,48)(41,43);(1,3)(2,6)(4,14)(5,10)(7,16)(8,15)(9,12)(11,13)(17,20,23,37)(18,25,28,40)(19,30,33,46)(21,36,22,35)(24,38,39,48)(26,41,27,34)(29,43,42,47)(31,45,32,44);(17,21,23,22)(18,26,28,27)(19,31,33,32)(20,35,37,36)(24,29,39,42)(25,34,40,41)(30,44,46,45)(38,47,48,43)

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, 12046);