#557×C₆₇ #16863085

order	4288
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₆₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

#557×C₆₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 83 points:

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

Conjugacy classes & character table

1675 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₆₇×#1626, C₆₇×#1636, C₆₇×#1648, …
maximal normal subgroup of	C₆₇×#1626, C₆₇×#1636, C₆₇×#1648, …
maximal quotient of	Q₈×C₄⋊C₄×C₆₇, C₆₇×#2351, C₆₇×#2355, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4288, 238);

#557×C67 #16863085