C₂×C₃₁×#479 #16843008

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×#479

Subgroups

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

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 4 generators on 57 points:

(1,2)(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);(3,4,6,8)(5,9,10,7)(11,12,14,16)(13,19,20,26)(15,23,22,18)(17,24,25,21);(3,5,6,10)(4,7,8,9)(12,16)(17,25)(18,23)(19,26);(11,13,14,20)(12,17,16,25)(15,24,22,21)(18,26,23,19)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9246, C₄×C₃₁×#479, C₃₁×#21618, …
maximal normal subgroup of	C₃₁×#9246, C₄×C₃₁×#479, C₃₁×#21618, …
maximal quotient of	C₂×C₃₁×#1805, C₂×C₃₁×#1863, C₂×C₃₁×#1865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1807);

C2×C31×#479 #16843008