C₇₃×#13360 #32922764

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₃×#13360

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇₃
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂×C₄×C₇₃ ◁ C₂×#41×C₇₃ ◁ G

702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 94 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)(3,12)(4,17)(5,8)(6,11)(7,14)(9,21)(10,22)(13,30)(15,29)(16,27)(18,25)(19,28)(20,26)(23,32)(24,31)(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)(2,7)(4,18)(5,13)(6,16)(8,24)(9,27)(10,23)(11,25)(12,17)(14,21)(15,22)(19,32)(20,31)(26,29)(28,30);(2,8)(3,13)(5,22)(9,26)(10,11)(12,27)(14,32)(15,16)(17,28)(18,31)(19,20)(23,24)

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, 6348);