D₃×C₁₉×C₂₉ #15693252

order	3306
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉×C₂₉
unambiguous semidirect product	C₃⋊(C₂×C₁₉×C₂₉)

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₂₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₉×C₂₉
Hall	C₃×C₂₉ ⋊ C₂×C₁₉
Hall	C₃×C₁₉ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₂₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₁₉×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₉×C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1653

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₃×C₁₉×C₂₉, C₁₉×C₂₉×D₁₅, D₃×C₇×C₁₉×C₂₉, …
maximal normal subgroup of	C₅×D₃×C₁₉×C₂₉, D₃×C₇×C₁₉×C₂₉, D₃×C₁₉×C₂₉⋊C₇, …
maximal quotient of	C₅×D₃×C₁₉×C₂₉, C₁₉×C₂₉×D₁₅, D₃×C₇×C₁₉×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3306, 6);

D3×C19×C29 #15693252