C₃₁×D₁₉ #11924366

order	1178
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₁₉
unambiguous semidirect product	C₁₉⋊(C₂×C₃₁)

Splittings

Fitting, socle, Hall	C₁₉×C₃₁ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₁₉×C₃₁	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 589

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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₉×D₃₁, C₂×C₃₁×D₁₉, C₃×C₃₁×D₁₉, …
maximal normal subgroup of	D₁₉×D₃₁, C₂×C₃₁×D₁₉, C₃×C₃₁×D₁₉, …
maximal quotient of	C₃₁×Dic₁₉, C₂×C₃₁×D₁₉, C₃×C₃₁×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1178, 1);

C31×D19 #11924366