C₂×C₃₁×#555 #16843406

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₂×C₃₁×#555

Subgroups

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

1240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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)(5,9)(6,10)(7,8)(12,13)(16,17);(4,8)(6,9)(11,12,15,13)(14,17,18,16);(3,5,7,10)(4,9,8,6)(11,13,15,12)(14,17,18,16);(3,6,7,9)(4,10,8,5)(11,14,15,18)(12,16,13,17)

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#8360, C₃₁×#8397, C₃₁×#8452, …
maximal normal subgroup of	C₃₁×#8360, C₃₁×#8397, C₃₁×#8452, …
maximal quotient of	C₂×C₃₁×#2346, C₂×C₃₁×#2354, C₂×C₃₁×#2363, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2205);

C2×C31×#555 #16843406