D₃×C₁₉⋊#3862 #30660854

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	D₃×C₁₉⋊#3862
unambiguous semidirect product	C₃⋊(C₂×C₁₉⋊#3862)
unambiguous semidirect product	(D₃×C₁₉)⋊#3862

Splittings

Fitting, socle, derived	C₃×C₇²×C₁₉ ⋊ C₂×C₃
Hall	C₃×C₁₉⋊#3862 ⋊ C₂
Hall	C₇²×C₁₉ ⋊ C₃×D₃
Sylow	C₇² ⋊ D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ D₃×#3862

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1197

A minimal faithful permutation representation — 2 generators on 36 points:

(2,3,5)(4,7,8)(6,10,9)(11,15,13)(12,16,14)(17,19,18)(21,22)(24,25,26)(27,29,28)(31,32,33)(34,36,35);(1,2,4,8,13,18,15,3,6,11,16,5,9,14,7,12,17,19,10)(20,21,22)(23,24,25,27,26,28,29)(30,31,33,35,32,34,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×#19150300, D₃×#19150301, D₃×#19150302, …
maximal normal subgroup of	D₃×#19150300, D₃×#19150301, D₃×#19150302, …
maximal quotient of	Dic₃×C₁₉⋊#3862, C₂×D₃×C₁₉⋊#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 381);

D3×C19⋊#3862 #30660854