C₂×C₃₁×#554 #16843405

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₃₁×#554

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

1200 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);(3,4,7,6)(5,9,10,8)(11,12,15,14)(13,17,18,16);(4,6)(8,9)(11,13,15,18)(12,16,14,17);(3,5)(4,8)(6,9)(7,10);(3,6,7,4)(5,9,10,8)(11,14,15,12)(13,16,18,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#8372, C₃₁×#8380, C₃₁×#8395, …
maximal normal subgroup of	C₃₁×#8372, C₃₁×#8380, C₃₁×#8395, …
maximal quotient of	C₂×C₃₁×#2345, C₂×D₄×C₄⋊C₄×C₃₁, C₂×C₃₁×#2349, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2204);

C2×C31×#554 #16843405