C₂×#124×C₇₁ #17985657

order	4544
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×#124×C₇₁

Subgroups

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

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 85
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 4 generators on 85 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇₁×#1469, C₂×#329×C₇₁, C₇₁×#1527, …
maximal normal subgroup of	C₇₁×#1469, C₂×#329×C₇₁, C₇₁×#1527, …
maximal quotient of	C₂×#382×C₇₁, C₂×#388×C₇₁, C₂×#390×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 207);

C2×#124×C71 #17985657