C₇₃×#7073 #32916477

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇₃×#7073

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₃	#102
commutator	C₂×C₈	C₂×C₈×C₇₃
Frattini, cosocle	C₈²	C₂²×C₇₃
socle, prime radical	C₂²×C₇₃	D₄⋊C₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₃ ◁ C₄×C₈×C₇₃ ◁ C₈²×C₇₃ ◁ G

132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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 — 2 generators on 105 points:

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

Conjugacy classes & character table

4234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 61);