C₆₇×#32948 #30712199

order	17152
nilpotency class	3
isoclinism	isoclinic class of #32947
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₆₇×#32948

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂²×C₄×C₆₇ ◁ G

1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.

normal subgroups only

This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 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:

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

Conjugacy classes & character table

3082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 25936);