C₂²×Q₁₆×C₇₁ #17985702

order	4544
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂²×Q₁₆×C₇₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₁	D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₇₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 4 generators on 91 points:

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

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1878, C₇₁×#1969, C₇₁×#1971, …
maximal normal subgroup of	C₇₁×#1878, C₇₁×#1969, C₇₁×#1971, …
maximal quotient of	C₂²×#103×C₇₁, C₂²×#107×C₇₁, C₂×C₄×Q₁₆×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 252);

C22×Q16×C71 #17985702