C₂×C₃₁×#551 #16843402

order	3968
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₃₁×#551

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

1328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 992

A minimal faithful permutation representation — 5 generators on 49 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12761, C₃₁×#17412, C₃₁×#17422, …
maximal normal subgroup of	C₃₁×#12761, C₃₁×#17412, C₃₁×#17422, …
maximal quotient of	C₂×C₃₁×#2342, C₂×C₃₁×#2343, C₂×C₃₁×#2353, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2201);

C2×C31×#551 #16843402