#475×C₆₇ #16863003

order	4288
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

#475×C₆₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄²×C₆₇ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 4288

A minimal faithful permutation representation — 3 generators on 83 points:

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

Conjugacy classes & character table

1273 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₆₇×#1640, C₆₇×#1642, C₆₇×#1643, …
maximal normal subgroup of	C₆₇×#1640, C₆₇×#1642, C₆₇×#1643, …
maximal quotient of	C₆₇×#1803, C₆₇×#1865, C₆₇×#1919, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 156);

#475×C67 #16863003