C₂×C₃₁×#576 #16843514

order	3968
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₁ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₃₁×#576

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₃₁
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ G

1512 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)(5,9)(6,8)(7,11)(10,14)(12,16)(13,15)(17,18);(4,8)(6,14)(9,15)(10,11)(13,18)(16,17);(3,5)(4,9)(6,13)(7,12)(8,15)(10,17)(11,16)(14,18);(5,12)(9,16)(13,18)(15,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#12741, C₃₁×#12743, C₃₁×#12748, …
maximal normal subgroup of	C₃₁×#12741, C₃₁×#12743, C₃₁×#12748, …
maximal quotient of	C₂×C₃₁×#2897, C₂×C₃₁×#2913, C₂×C₃₁×#2946, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2313);

C2×C31×#576 #16843514