C₆₇×#23896 #30703147

order	17152
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₆₇×#23896

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#2403
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₆₇
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂⁴×C₆₇ ◁ G

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 conjugacy classes of subgroups — too many to draw. Only its 282 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)(3,7)(4,8)(5,9)(6,10)(11,17)(12,18)(13,19)(14,27)(15,22)(16,23)(20,25)(21,28)(24,31)(26,30)(29,32)(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);(1,3,6,13)(2,7,10,19)(4,11,15,25)(5,12,16,26)(8,20,22,17)(9,18,23,30)(14,24,28,32)(21,31,27,29);(1,4)(2,8)(3,11)(5,14)(6,15)(7,17)(9,21)(10,22)(12,24)(13,25)(16,28)(18,29)(19,20)(23,27)(26,32)(30,31);(1,5)(2,9)(3,12)(4,14)(6,16)(7,18)(8,21)(10,23)(11,24)(13,26)(15,28)(17,29)(19,30)(20,31)(22,27)(25,32)

Conjugacy classes & character table

2680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 16884);