C₃₁×C₃⋊C₁₆ #13093407

order	1488
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₆×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₁₆×C₃₁)

Splittings

derived, Sylow	C₃ ⋊ C₁₆×C₃₁
Hall	C₃×C₃₁ ⋊ C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₈×C₃₁	D₃
commutator, hypocenter	C₃	C₁₆×C₃₁
Frattini	C₈	D₃×C₃₁
Fitting	C₃×C₈×C₃₁	C₂
socle, prime radical	C₂×C₃×C₃₁	C₈
cosocle	C₃×C₈	C₂×C₃₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₈×C₃₁

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 1488

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(33,34)(35,36,37,40,38,41,43,46,39,42,44,47,45,48,49,50);(32,33,34)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 3);

C31×C3⋊C16 #13093407