C₂×C₇₃×#1318 #32920833

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₇₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₇₃×#1318

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₃	#99
commutator	C₂×C₄	C₂²×C₈×C₇₃
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₇₃
prime radical	C₂³×D₄×C₇₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂⁴×C₇₃ ◁ C₂²×C₄⋊C₄×C₇₃ ◁ G

834 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 91
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(3,4,5,7,6,8,9,10)(11,12)(13,16,18,15)(14,17);(12,15)(13,18)(16,17)

Conjugacy classes & character table

3796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 4417);