C₆₇×#10086 #30689337

order	17152
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₆₇×#10086

Subgroups

	subgroup	G/H
center, socle	C₂³×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
prime radical	C₂²×D₄×C₆₇	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

542 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 95
transitive degree	μ_t(G) = 8576

A minimal faithful permutation representation — 3 generators on 95 points:

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

Conjugacy classes & character table

2278 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 3074);