Finite Group Databasebeta

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C₉×C₄₇×Dic₁₉ #44565244

order	32148
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₄₇×Dic₁₉

Splittings

derived, Sylow	C₁₉ ⋊ C₄×C₉×C₄₇
Hall	C₉×C₁₉×C₄₇ ⋊ C₄
Hall	C₁₉×C₄₇ ⋊ C₄×C₉
Hall	C₉×C₁₉ ⋊ C₄×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₄₇	D₁₉
commutator, hypocenter	C₁₉	C₄×C₉×C₄₇
Frattini	C₂×C₃	C₃×D₁₉×C₄₇
Fitting	C₂×C₉×C₁₉×C₄₇	C₂
socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂×C₃
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₄₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₉×C₄₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32148

Conjugacy classes & character table

9306 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 4);