C₂×C₇₃×#2030 #32932870

order	18688
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₇₃×#2030

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₃	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇₃
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂⁵×C₇₃ ◁ G

1482 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 1482 conjugacy classes of subgroups — too many to draw. Only its 350 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) = 99
transitive degree	μ_t(G) = 4672

A minimal faithful permutation representation — 4 generators on 99 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(3,4,6,8)(5,9,10,7)(11,12)(13,16)(14,17)(15,18)(19,24)(20,23)(21,25)(22,26);(3,5,6,10)(4,7,8,9)(11,13)(12,16)(14,19)(15,20)(17,24)(18,23)(21,26)(22,25);(11,14,15,21)(12,17,18,25)(13,19,20,26)(16,22,23,24)

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, 16454);