C₆₇×#10134 #30689385

order	17152
nilpotency class	3
isoclinism	isoclinic class of #10128
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#10134

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
prime radical	#532×C₆₇	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

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

normal subgroups only

This group has 456 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) = 99
transitive degree	μ_t(G) = 8576

A minimal faithful permutation representation — 3 generators on 99 points:

(3,9)(4,11)(6,14)(7,12)(10,13)(15,16)(17,18,22,26)(19,27,30,31)(20,25,21,24)(23,29,32,28)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2,5,8)(3,6,10,15)(4,12,11,7)(9,16,13,14)(17,19,22,30)(18,23,26,32)(20,29,21,28)(24,31,25,27);(1,3)(2,6)(4,13)(5,10)(7,16)(8,15)(9,11)(12,14)(18,24)(19,28)(20,21)(25,26)(27,31)(29,30)

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, 3122);