C₂×C₃₁×#436 #16842861

order	3968
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₁×#436

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂³
commutator	C₂²	C₂³×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂²×C₄
prime radical	C₂²×D₄×C₃₁	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 4 generators on 45 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);(3,4)(5,6)(7,8,11,9,10,12,14,13);(4,6)(8,12)(9,13);(7,9,11,12,10,13,14,8)

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8166, C₃₁×#8206, C₃₁×#8208, …
maximal normal subgroup of	C₃₁×#8166, C₃₁×#8206, C₃₁×#8208, …
maximal quotient of	C₂×C₃₁×#1589, C₂×C₃₁×#1590, C₂×C₃₁×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1660);

C2×C31×#436 #16842861