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C₃×Dic₃₉ #90850

order	468
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₃₉
unambiguous semidirect product	C₃⋊(C₃×Dic₁₃)

Splittings

derived	C₃×C₁₃ ⋊ C₃×C₄
Hall	C₃²×C₁₃ ⋊ C₄
Sylow	C₁₃ ⋊ C₃×Dic₃
Sylow	C₃² ⋊ Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₉
commutator, hypocenter	C₃×C₁₃	C₃×C₄
Frattini	C₂	C₃×D₃₉
Fitting, socle, prime radical	C₂×C₃²×C₁₃	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₃

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 156

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3)(5,6)(7,10,9,8)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23);(4,5,6)(11,12,14,16,18,20,22,23,21,19,17,15,13)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×Dic₃×D₁₃, C₃×D₃×Dic₁₃, C₃×#64602, …
maximal normal subgroup of	C₃×Dic₃×D₁₃, C₃×D₃×Dic₁₃, C₃×#64602, …
maximal quotient of	C₃×C₃⋊#1055, C₂×C₃×Dic₃₉, C₃×Dic₁₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 25);