#563×C₇₁ #17985694

order	4544
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

#563×C₇₁

Subgroups

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

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 4 generators on 95 points:

(2,5)(3,7)(9,10,14,12)(11,17,19,15)(13,20,22,16)(18,23,21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,5)(6,8)(9,11,14,19)(10,15,12,17)(13,21,22,18)(16,24,20,23);(1,2)(3,6)(4,5)(7,8)(9,12,14,10)(11,15,19,17)(13,20,22,16)(18,23,21,24);(1,3)(2,6)(4,7)(5,8)(9,13)(10,16)(11,18)(12,20)(14,22)(15,23)(17,24)(19,21)

Conjugacy classes & character table

1349 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1657, C₇₁×#1660, C₇₁×#1664, …
maximal normal subgroup of	C₇₁×#1657, C₇₁×#1660, C₇₁×#1664, …
maximal quotient of	C₇₁×#2376, C₇₁×#2378, C₇₁×#2379, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 244);

#563×C71 #17985694