C₂×#131×C₇₁ #17985698

order	4544
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×#131×C₇₁

Subgroups

	subgroup	G/H
center	C₂×C₈×C₇₁	C₂²
commutator	C₂	C₂³×C₄×C₇₁
Frattini, cosocle	C₄	C₂⁴×C₇₁
socle	C₂²×C₇₁	C₂²×C₄
prime radical	C₂×#41×C₇₁	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₇₁ ◁ G

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 4 generators on 89 points:

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

Conjugacy classes & character table

2840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1757, C₇₁×#1764, C₇₁×#1765, …
maximal normal subgroup of	C₇₁×#1757, C₇₁×#1764, C₇₁×#1765, …
maximal quotient of	C₂×#405×C₇₁, C₄×#131×C₇₁, C₂×#408×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 248);

C2×#131×C71 #17985698