C₂×C₃₁×#394 #16842319

order	3968
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂×C₃₁×#394

Subgroups

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

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×#9018, C₃₁×#9019, C₃₁×#9915, …
maximal normal subgroup of	C₃₁×#9018, C₃₁×#9019, C₃₁×#9915, …
maximal quotient of	C₂×C₃₁×#1438, C₂×C₃₁×#1439, C₂×C₃₁×#1440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1118);

C2×C31×#394 #16842319