C₁₉×#887 #14269639

order	1824
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₉×#887

Splittings

Hall	C₃×C₁₉ ⋊ C₄×Q₈
Sylow	C₃ ⋊ C₄×Q₈×C₁₉

Subgroups

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	C₂³
cosocle	C₂²×C₃	C₂³×C₁₉
hypercenter	C₄⋊C₄×C₁₉	D₃
hypocenter	C₃	C₄×Q₈×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄⋊C₄×C₁₉

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1824

A minimal faithful permutation representation — 3 generators on 34 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22)(23,25,26,24)(29,33)(31,34);(27,29,30,33)(28,31,32,34);(21,22)(23,24,26,25)(27,28,30,32)(29,31,33,34)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1824, 866);

C19×#887 #14269639