C₇₃×#20773 #32930177

order	18688
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₇₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₃×#20773

Subgroups

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

830 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 382 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 — 4 generators on 105 points:

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

Conjugacy classes & character table

4672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 13761);