C₆₇×#11669 #30690920

order	17152
nilpotency class	4
isoclinism	isoclinic class of #11669
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₇×#11669

Subgroups

	subgroup	G/H
center	C₄×C₆₇	#418
commutator	C₂×C₈	C₂²×C₄×C₆₇
Frattini, cosocle	C₄×C₈	C₂³×C₆₇
socle	C₂×C₆₇	#1490
prime radical	#575×C₆₇	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₆₇ ◁ C₂×C₈×C₆₇ ◁ C₄×M₁₆×C₆₇ ◁ G

360 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 106 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 — 3 generators on 83 points:

(1,2,4,11,7,12,16,10,8,13,5,15,6,3,14,9)(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)(2,7)(4,9)(5,10)(6,13)(8,12)(11,16)(14,15);(1,4,6,14,8,5,7,16)(2,9,12,11,13,10,3,15)

Conjugacy classes & character table

3082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 4657);