C₆₇×#32873 #30712124

order	17152
nilpotency class	3
isoclinism	isoclinic class of #32873
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₆₇×#32873

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2840
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂⁴×C₆₇ ◁ G

854 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 186 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) = 83
transitive degree	μ_t(G) = 1072

A minimal faithful permutation representation — 4 generators on 83 points:

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

Conjugacy classes & character table

1876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 25861);