D₃×#14584116 #30660850

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#14584116
unambiguous semidirect product	C₃⋊(C₂×#14584116)

Splittings

Fitting, socle, derived	C₃×C₇²×C₁₉ ⋊ C₂×C₃
Hall	C₃×#14584116 ⋊ C₂
Hall	C₇²×C₁₉ ⋊ C₃×D₃
Sylow	C₇² ⋊ D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ D₃×#3861

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

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 2793

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×#19150312, D₃×#19150285, D₃×#19150287, …
maximal normal subgroup of	D₃×#19150312, D₃×#19150285, D₃×#19150287, …
maximal quotient of	Dic₃×#14584116, C₂×D₃×#14584116

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 377);

D3×#14584116 #30660850