C₆₇×#10084 #30689335

order	17152
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#10084

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

484 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 103
transitive degree	μ_t(G) = 17152

A minimal faithful permutation representation — 3 generators on 103 points:

(5,6,11,16)(7,17,8,19)(9,15,10,14)(12,20,13,18)(21,22,26,24)(23,29,32,36)(25,33,35,28)(27,34,30,31)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,2)(3,4)(5,7)(6,12)(8,11)(9,20)(10,18)(13,16)(14,19)(15,17)(21,23,26,32)(22,27,24,30)(25,34,35,31)(28,36,33,29);(2,4)(5,8,11,7)(6,13,16,12)(9,20,10,18)(14,19,15,17)(21,24,26,22)(23,30,32,27)(25,28,35,33)(29,34,36,31)

Conjugacy classes & character table

2278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 3072);