C₁₉×#829 #14268982

order	1824
isoclinism	isoclinic class of #826
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#829

Splittings

Hall	C₃×C₁₉ ⋊ Q₃₂
Sylow	C₃ ⋊ C₁₉×Q₃₂

Subgroups

	subgroup	G/H
center	C₂×C₁₉	#213
commutator, cosocle	C₃×C₈	C₂²×C₁₉
Frattini	C₈	C₂×D₃×C₁₉
Fitting	C₃×Q₁₆×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₉	D₈
hypercenter	Q₁₆×C₁₉	D₃
hypocenter	C₃	C₁₉×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₄×C₁₉ ◁ C₈×C₁₉ ◁ Q₁₆×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 1824

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22)(23,25,28,36)(24,29,32,46)(26,38,41,54)(27,43,39,35)(30,48,49,53)(31,50,42,45)(33,51,52,37)(34,47,44,40);(21,22)(23,24,28,32)(25,33,36,52)(26,37,41,51)(27,42,39,31)(29,44,46,34)(30,47,49,40)(35,53,43,48)(38,50,54,45)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 209);

C19×#829 #14268982