C₂×C₇₃×#2202 #32942966

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

Aliases

direct product

C₂×C₇₃×#2202

Subgroups

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

1284 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1284 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)(5,8)(6,9)(7,12)(10,13)(11,15)(14,17)(16,18);(4,8)(5,13)(6,15)(9,17)(10,12)(11,18);(4,9)(6,15)(8,17)(10,18)(11,12)(14,16)

Conjugacy classes & character table

2482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 26550);