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C₃×C₇×Dic₃×C₁₉ #18012201

order	4788
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₇×Dic₃×C₁₉
unambiguous semidirect product	C₃⋊(C₃×C₄×C₇×C₁₉)

Splittings

derived	C₃ ⋊ C₃×C₄×C₇×C₁₉
Hall	C₃²×C₇×C₁₉ ⋊ C₄
Hall	C₃²×C₁₉ ⋊ C₄×C₇
Hall	C₃²×C₇ ⋊ C₄×C₁₉
Sylow	C₃² ⋊ C₄×C₇×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₉	D₃
commutator, hypocenter	C₃	C₃×C₄×C₇×C₁₉
Frattini	C₂	C₃×D₃×C₇×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₉	C₂
cosocle	C₂×C₃	C₂×C₃×C₇×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₇×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1596

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₇×C₁₉×Dic₁₅, C₃×C₅×C₇×Dic₃×C₁₉, C₃×C₇×C₁₉×ΓL(1,𝔽₁₆), …
maximal normal subgroup of	C₃×C₅×C₇×Dic₃×C₁₉, C₃×Dic₃×C₁₉×C₄₉, C₃×C₇²×Dic₃×C₁₉
maximal quotient of	C₃×C₇×C₁₉×Dic₁₅, C₃×C₅×C₇×Dic₃×C₁₉, C₃×C₇×C₁₉×ΓL(1,𝔽₁₆), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 117);