C₂×C₃₁×#536 #16843380

order	3968
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₃₁×#536

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
prime radical	C₂²×#41×C₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1984

A minimal faithful permutation representation — 5 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)(8,12)(9,15)(10,18)(20,22);(7,8,11,12)(9,16,15,13)(10,14,18,19)(17,22,21,20);(3,4)(5,6)(7,9,11,15)(8,13,12,16)(10,17,18,21)(14,20,19,22);(7,10)(8,14)(9,17)(11,18)(12,19)(13,20)(15,21)(16,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#8520, C₃₁×#8524, C₃₁×#10974, …
maximal normal subgroup of	C₃₁×#8520, C₃₁×#8524, C₃₁×#10974, …
maximal quotient of	C₂×C₃₁×#2310, C₂×C₃₁×#2311, C₂×C₃₁×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2179);

C2×C31×#536 #16843380