C₁₉×D₃₁ #11924367

order	1178
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₃₁
unambiguous semidirect product	C₃₁⋊(C₂×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₉×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₁₉

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);(21,50)(22,49)(23,48)(24,47)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₉×D₃₁, C₂×C₁₉×D₃₁, C₃×C₁₉×D₃₁, …
maximal normal subgroup of	D₁₉×D₃₁, C₂×C₁₉×D₃₁, C₃×C₁₉×D₃₁, …
maximal quotient of	C₁₉×Dic₃₁, C₂×C₁₉×D₃₁, C₃×C₁₉×D₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1178, 2);

C19×D31 #11924367