#564×C₇₁ #17985695

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

Aliases

direct product

#564×C₇₁

Subgroups

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

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 4 generators on 103 points:

(3,9)(4,12)(6,10)(7,14)(17,18,21,24)(19,22,27,25)(20,28,29,23)(26,31,32,30)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,2,5,8)(3,10,9,6)(4,7,12,14)(11,16,15,13)(17,18)(19,25)(20,28)(21,24)(22,27)(23,29)(26,30)(31,32);(1,3,5,9)(2,6,8,10)(4,11,12,15)(7,13,14,16)(17,19)(18,22)(20,26)(21,27)(23,30)(24,25)(28,31)(29,32);(1,4)(2,7)(3,11)(5,12)(6,13)(8,14)(9,15)(10,16)(17,20,21,29)(18,23,24,28)(19,26,27,32)(22,30,25,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1658, C₇₁×#1663, C₂×#564×C₇₁, …
maximal normal subgroup of	C₇₁×#1658, C₇₁×#1663, C₂×#564×C₇₁, …
maximal quotient of	C₇₁×#2382, C₇₁×#2719, C₇₁×#2726, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 245);

#564×C71 #17985695