C₂×C₃₁×#547 #16843397

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₃₁×#547

Subgroups

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

1632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#8364, C₃₁×#8376, C₃₁×#8387, …
maximal normal subgroup of	C₃₁×#8364, C₃₁×#8376, C₃₁×#8387, …
maximal quotient of	C₂×C₃₁×#2339, C₂×C₃₁×#2344, C₂×D₄×C₄⋊C₄×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2196);

C2×C31×#547 #16843397