#472×C₆₇ #16863000

order	4288
nilpotency class	3
isoclinism	isoclinic class of #471
automorphism	?
homology	Abelianization (H₁) = C₂³×C₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#472×C₆₇

Subgroups

	subgroup	G/H
center, socle	C₂×C₆₇	#121
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₆₇ ◁ C₂×C₄×C₆₇ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 1072

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

(2,6)(3,10)(4,7)(9,14)(11,12)(13,15)(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);(1,2,7,14,5,9,4,6)(3,8,10,15,12,16,11,13);(1,3)(2,8)(4,11)(5,12)(6,13)(7,10)(9,16)(14,15)

Conjugacy classes & character table

1072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₆₇×#2192, C₆₇×#2193, C₆₇×#2221, …
maximal normal subgroup of	C₆₇×#2192, C₆₇×#2193, C₆₇×#2221, …
maximal quotient of	C₆₇×#1667, C₆₇×#1668, C₆₇×#1675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 153);

#472×C67 #16863000