C₃₁⋊C₁₆ #92466

order	496
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product

C₃₁⋊C₁₆

Splittings

derived, Sylow

C₃₁ ⋊ C₁₆

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₈	D₃₁
commutator, hypocenter	C₃₁	C₁₆
Fitting, cosocle	C₈×C₃₁	C₂
socle, prime radical	C₂×C₃₁	C₈
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₈

10 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 2 generators on 47 points:

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

Polycyclic presentation:

2^4,31|a^2=b,b^2=c,c^2=d,e^a=e^30

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₆×D₃₁, #11758386, C₂×C₃₁⋊C₁₆, …
maximal normal subgroup of	C₁₆×D₃₁, #11758386, C₂×C₃₁⋊C₁₆, …
maximal quotient of	C₃₁⋊C₃₂, C₂×C₃₁⋊C₁₆, C₃×C₃₁⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 1);

C31⋊C16 #92466