C₇₃×#11859 #32921263

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₇₃×#11859

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₇₃
Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
prime radical	C₂³×C₇₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 4672

A minimal faithful permutation representation — 3 generators on 121 points:

(1,2)(3,9,11,6)(4,7)(5,8)(10,15,12,14)(13,16)(17,18)(19,29)(20,26)(21,36)(22,38)(23,28)(24,31)(25,34)(27,37)(30,46)(32,40)(33,43)(35,45)(39,44)(41,48)(42,47)(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);(1,3)(2,6)(4,12)(5,11)(7,15)(8,9)(10,13)(14,16)(17,19,23,33)(18,24,28,42)(20,31,35,47)(21,30,34,48)(22,39,37,32)(25,43,36,29)(26,44,45,40)(27,46,38,41);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,20,22,34,23,35,37,21)(18,25,27,26,28,36,38,45)(19,30,32,47,33,48,39,31)(24,40,41,29,42,44,46,43)

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, 4847);