C₂×C₃₁×#494 #16843078

order	3968
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₃₁×#494

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

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3968

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(4,6)(7,8,11,14)(9,15,18,22)(10,19,16,13)(12,20,21,17);(7,9,16,20,11,18,10,17)(8,12,19,22,14,21,13,15);(3,4,5,6)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9066, C₃₁×#9733, C₃₁×#9742, …
maximal normal subgroup of	C₃₁×#9066, C₃₁×#9733, C₃₁×#9742, …
maximal quotient of	C₂×C₃₁×#1707, C₂×C₃₁×#1710, C₂×C₃₁×#1713, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1877);

C2×C31×#494 #16843078