C₆₇×#9932 #30689183

order	17152
nilpotency class	3
isoclinism	isoclinic class of #9930
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#9932

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₇	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
prime radical	C₆₇×#3192	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

610 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 4288

A minimal faithful permutation representation — 3 generators on 91 points:

(2,6)(3,4)(7,8)(9,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,23)(22,24)(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);(1,2)(3,8)(4,6)(5,7)(9,11,13,18)(10,14,16,21)(12,17,19,24)(15,22,23,20);(1,2)(3,6)(4,8)(5,7)(9,12)(10,15)(11,17)(13,19)(14,20)(16,23)(18,24)(21,22)

Conjugacy classes & character table

2077 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 2920);