C₃×C₃₁⋊C₁₆ #13093408

order	1488
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₃₁⋊C₁₆

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈	D₃₁
commutator, hypocenter	C₃₁	C₃×C₁₆
Frattini	C₈	C₃×D₃₁
Fitting	C₃×C₈×C₃₁	C₂
socle, prime radical	C₂×C₃×C₃₁	C₈
cosocle	C₈×C₃₁	C₂×C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₈

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1488, 4);

C3×C31⋊C16 #13093408