C₇₃×#12175 #32921579

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

Aliases

direct product

C₇₃×#12175

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#1598
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₇₃
prime radical	C₇₃×#2190	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×M₁₆×C₇₃ ◁ G

346 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 70 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)(4,17)(5,9)(6,11)(7,12)(8,14)(10,20)(15,29)(16,30)(18,23)(19,28)(21,27)(22,26)(24,32)(25,31)(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)(2,8)(4,18)(5,15)(6,22)(7,16)(9,23)(10,26)(11,24)(12,25)(13,17)(14,20)(19,32)(21,31)(27,29)(28,30);(2,9,12,11)(4,19)(8,23,25,24)(10,17,27,28)(13,29,30,26)(14,31)(18,32)(20,21)

Conjugacy classes & character table

1825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 5163);