C₂×C₃₁×#400 #16842327

order	3968
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₃₁×#400

Subgroups

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

604 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);(9,13)(11,14)(15,16,18,20)(17,21,22,19);(4,6)(7,8,10,12)(9,14,13,11)(15,16)(17,21)(18,20)(19,22);(3,4)(5,6)(7,9)(8,11)(10,13)(12,14)(15,17,18,22)(16,19,20,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#9022, C₃₁×#9023, C₃₁×#9921, …
maximal normal subgroup of	C₃₁×#9022, C₃₁×#9023, C₃₁×#9921, …
maximal quotient of	C₂×C₃₁×#1441, C₂×C₃₁×#1442, C₂×C₃₁×#1443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1126);

C2×C31×#400 #16842327