C₇₃×#13436 #32922840

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₇₃×#13436

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇₃
prime radical	C₇₃×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

438 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 2336

A minimal faithful permutation representation — 3 generators on 105 points:

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

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 6424);