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C₅×C₉×D₅×D₁₉ #30685574

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₅×C₉×D₅×D₁₉

Splittings

Fitting, Hall	C₅²×C₉×C₁₉ ⋊ C₂²
derived	C₅×C₁₉ ⋊ C₂²×C₅×C₉
Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×C₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×C₅×D₅
Sylow	C₅² ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₅×C₉×D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₅×D₁₉
commutator, hypocenter	C₅×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₃×C₅×D₅×D₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×C₅×D₅×D₁₉	C₃
cosocle	C₃×C₅×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅×C₉

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 211);