C₆₇×#13705 #30692956

order	17152
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₇×#13705

Subgroups

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₆₇
prime radical	C₂×D₁₆×C₆₇	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄²×C₆₇ ◁ C₄×C₈×C₆₇ ◁ C₄×C₁₆×C₆₇ ◁ G

176 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 107
transitive degree	μ_t(G) = 8576

A minimal faithful permutation representation — 3 generators on 107 points:

(1,2,4,6)(3,7,8,5)(9,10,14,19)(11,15,23,30)(12,24,26,40)(13,27,25,18)(16,31,33,20)(17,34,35,21)(22,36,37,29)(28,39,32,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3,4,8)(2,5,6,7);(10,15)(11,20)(12,21)(13,25)(16,17)(18,36)(19,30)(22,39)(23,31)(24,28)(26,34)(27,29)(32,40)(33,35)(37,38)

Conjugacy classes & character table

3283 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 6693);