#510×C₇₁ #17985641

order	4544
nilpotency class	4
isoclinism	isoclinic class of #509
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#510×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂³×C₇₁
prime radical	#135×C₇₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂×C₈×C₇₁ ◁ G

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 3 generators on 103 points:

(1,2)(3,11)(4,15)(5,20)(6,8)(7,12)(9,18)(10,17)(13,31)(14,28)(16,26)(19,27)(21,25)(22,30)(23,32)(24,29)(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);(1,3,6,14)(2,7,8,22)(4,16,19,32)(5,21,17,13)(9,25,24,31)(10,26,20,23)(11,27,28,15)(12,29,30,18);(2,8)(7,22)(9,24)(10,20)(11,28)(15,27)(23,26)(25,31)

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#2180, C₇₁×#2191, C₇₁×#2194, …
maximal normal subgroup of	C₇₁×#2180, C₇₁×#2191, C₇₁×#2194, …
maximal quotient of	C₇₁×#2139, C₇₁×#2141, C₇₁×#2159, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 191);

#510×C71 #17985641