C₂³×D₁₆×C₇₃ #32972029

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₇₃ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

C₂³×D₁₆×C₇₃

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₇₃	D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₇₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ C₂³×C₈×C₇₃ ◁ G

2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

normal subgroups only

This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 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) = 95
transitive degree	μ_t(G) = 9344

A minimal faithful permutation representation — 5 generators on 95 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(3,4);(5,6);(7,8)(9,12)(10,19)(11,15)(13,16)(14,17)(18,21)(20,22);(8,12)(9,16)(10,17)(13,14)(15,21)(18,22)(19,20)

Conjugacy classes & character table

6424 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 55613);