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C₃×C₁₉×Dic₁₅ #16811866

order	3420
isoclinism	isoclinic class of D₁₅
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×Dic₁₅
unambiguous semidirect product	C₃⋊(C₃×C₁₉×Dic₅)

Splittings

derived	C₃×C₅ ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₅×C₁₉ ⋊ C₄
Hall	C₃²×C₁₉ ⋊ Dic₅
Hall	C₅×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₅ ⋊ C₄×C₁₉
Sylow	C₃² ⋊ C₁₉×Dic₅
Sylow	C₅ ⋊ C₃×Dic₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₅
commutator, hypocenter	C₃×C₅	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×D₁₅
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₉	C₂
cosocle	C₂×C₃×C₅	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1140

Conjugacy classes & character table

1026 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₉×Dic₇₅, C₃×C₅×C₁₉×Dic₁₅, C₃×C₁₉×C₃⋊#1039, …
maximal normal subgroup of	C₃×C₅×C₁₉×Dic₁₅, C₃×C₇×C₁₉×Dic₁₅, C₃×C₁₁×C₁₉×Dic₁₅
maximal quotient of	C₃×C₁₉×Dic₇₅, C₃×C₅×C₁₉×Dic₁₅, C₃×C₁₉×C₃⋊#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3420, 59);