C₆₇×#32877 #30712128

order	17152
nilpotency class	3
isoclinism	isoclinic class of #32875
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#32877

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

594 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 186 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 — 4 generators on 99 points:

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

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, 25865);