C₇₃×#23470 #32932874

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₇₃×#23470

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇₃
prime radical	C₂⁴×C₇₃	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

1178 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 334 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) = 113
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 4 generators on 113 points:

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

Conjugacy classes & character table

3358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 16458);