C₂×C₃₁×H(3,ℤ/4) #16841663

order	3968
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂×C₃₁×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₁	C₄²
commutator	C₄	C₂×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	#95
prime radical	C₂⁴×C₃₁	D₄
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ G

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₁×#7254, C₃₁×#7256, C₄×C₃₁×H(3,ℤ/4), …
maximal normal subgroup of	C₃₁×#7254, C₃₁×#7256, C₄×C₃₁×H(3,ℤ/4), …
maximal quotient of	C₂×C₃₁×#1274, C₃₁×#7854, C₃₁×#7855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 462);

C2×C31×H(3,ℤ/4) #16841663