C₇₃×#23840 #32933244

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

Aliases

direct product

C₇₃×#23840

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 18688

A minimal faithful permutation representation — 4 generators on 105 points:

(1,2,5,8)(3,7,4,6)(9,10,13,16)(11,15,12,14)(17,18,21,24)(19,22,26,30)(20,23,28,32)(25,29,27,31)(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);(1,3,5,4)(2,6,8,7)(9,11,13,12)(10,14,16,15)(17,19)(18,22)(20,25)(21,26)(23,29)(24,30)(27,28)(31,32);(1,3,5,4)(2,7,8,6)(9,12,13,11)(10,15,16,14)(19,25)(20,28)(22,29)(23,32)(26,27)(30,31);(1,4,5,3)(2,6,8,7)(19,26)(22,30)(25,27)(29,31)

Conjugacy classes & character table

3796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 16828);