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C₂×C₁₉×C₃⋊(C₅⋊D₅) #19152906

order	5700
isoclinism	isoclinic class of C₃⋊(C₅⋊D₅)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₁₉×C₃⋊(C₅⋊D₅)
unambiguous semidirect product	(C₂×C₃)⋊(C₁₉×C₅⋊D₅)
unambiguous semidirect product	(C₂×C₅)⋊(C₁₉×D₁₅)

Splittings

Fitting, socle	C₂×C₃×C₅²×C₁₉ ⋊ C₂
derived, Hall	C₃×C₅² ⋊ C₂²×C₁₉
Hall	C₃×C₅²×C₁₉ ⋊ C₂²
Hall	C₅²×C₁₉ ⋊ C₂×D₃
Hall	C₃×C₁₉ ⋊ C₂×C₅⋊D₅
Sylow	C₅² ⋊ C₂×D₃×C₁₉
Sylow	C₃ ⋊ C₂×C₁₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊(C₅⋊D₅)
commutator, hypocenter	C₃×C₅²	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₁₉

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₉×C₅⋊D₄₅, C₂×C₁₉⋊C₃×C₃⋊(C₅⋊D₅), C₂×C₁₉×C₃⋊((C₅⋊D₅)⋊C₃), …
maximal normal subgroup of	C₂×C₁₉⋊C₃×C₃⋊(C₅⋊D₅), C₂×C₁₉×C₃⋊((C₅⋊D₅)⋊C₃), C₂×C₃⋊((C₅⋊D₅)⋊(C₁₉⋊C₃)), …
maximal quotient of	C₂×C₁₉×C₅⋊D₄₅, D₃×C₁₉×C₃⋊(C₅⋊D₅), C₂×C₁₉×C₃⋊(C₃⋊(C₅⋊D₅)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 163);