C₂×C₃₁×#543 #16843389

order	3968
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₃₁×#543

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

1296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 5 generators on 49 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);(3,4,7,10)(5,11,13,9)(6,8,14,16)(12,17,18,15);(4,8)(5,12)(10,16)(13,18);(3,5,7,13)(4,9,10,11)(6,12,14,18)(8,15,16,17);(4,8)(9,15)(10,16)(11,17)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8405, C₃₁×#11390, C₃₁×#11394, …
maximal normal subgroup of	C₃₁×#8405, C₃₁×#11390, C₃₁×#11394, …
maximal quotient of	C₂×C₃₁×#2315, C₂×C₃₁×#2329, C₄×C₃₁×#543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2188);

C2×C31×#543 #16843389