C₆₇×#7484 #30686735

order	17152
nilpotency class	5
isoclinism	isoclinic class of #7481
automorphism	?
homology	Abelianization (H₁) = C₄²×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₆₇×#7484

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#1390
commutator	C₂×Q₈	C₄²×C₆₇
Frattini, cosocle	#532	C₂²×C₆₇
prime radical	#532×C₆₇	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂×C₄×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ #532×C₆₇ ◁ G

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 2144

A minimal faithful permutation representation — 2 generators on 99 points:

(1,2,4,9,6,12,21,28)(3,13,15,7,18,23,31,25)(5,11,19,8,22,10,20,26)(14,29,17,27,32,24,16,30)(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);(1,3,5,16,6,18,22,17)(2,7,10,24,12,25,11,29)(4,14,19,31,21,32,20,15)(8,13,9,27,26,23,28,30)

Conjugacy classes & character table

1876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 472);