#550×C₇₁ #17985681

order	4544
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

#550×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ G

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 2272

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

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

Conjugacy classes & character table

1775 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1621, C₇₁×#1631, C₇₁×#1641, …
maximal normal subgroup of	C₇₁×#1621, C₇₁×#1631, C₇₁×#1641, …
maximal quotient of	C₇₁×#2341, Q₈×C₄⋊C₄×C₇₁, C₇₁×#2354, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 231);

#550×C71 #17985681