C₂×C₃₁×#478 #16843005

order	3968
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₃₁×#478

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1984

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

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#9245, C₄×C₃₁×#478, C₃₁×#21617, …
maximal normal subgroup of	C₃₁×#9245, C₄×C₃₁×#478, C₃₁×#21617, …
maximal quotient of	C₂×C₃₁×#1804, C₂×C₃₁×#1862, C₂×C₃₁×#1864, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1804);

C2×C31×#478 #16843005