C₂×C₇₃×#2205 #32942970

order	18688
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₇₃×#2205

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₇₃
prime radical	C₂×2₋¹⁺⁴×C₇₃	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₇₃ ◁ C₂²×Q₈×C₇₃ ◁ G

1136 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 2336

A minimal faithful permutation representation — 4 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)(5,13)(6,16)(7,11)(8,18)(9,14)(10,15)(12,17);(3,5,9,8)(4,10,14,16)(6,17,15,7)(11,13,12,18);(3,6,9,15)(4,11,14,12)(5,7,8,17)(10,18,16,13)

Conjugacy classes & character table

2920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 26554);