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C₉×D₁₉×D₄₇ #44565258

order	32148
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₁₉×D₄₇

Splittings

Fitting, Hall	C₉×C₁₉×C₄₇ ⋊ C₂²
derived, Hall	C₁₉×C₄₇ ⋊ C₂²×C₉
Hall	C₉×C₄₇ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₉×D₄₇
commutator, hypocenter	C₁₉×C₄₇	C₂²×C₉
Frattini	C₃	C₃×D₁₉×D₄₇
Fitting	C₉×C₁₉×C₄₇	C₂²
socle, cosocle	C₃×C₁₉×C₄₇	C₂²×C₃
prime radical	C₃×D₁₉×D₄₇	C₃
LCS	G ▷ C₁₉×C₄₇
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8037

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 18);