Finite Group Databasebeta

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C₉×C₁₉×D₇₃ #38735696

order	24966
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₉×D₇₃

Splittings

Fitting, Hall	C₉×C₁₉×C₇₃ ⋊ C₂
derived, Sylow	C₇₃ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₇₃ ⋊ C₂×C₉
Hall	C₉×C₇₃ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₇₃
commutator, hypocenter	C₇₃	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₇₃
Fitting	C₉×C₁₉×C₇₃	C₂
socle	C₃×C₁₉×C₇₃	C₂×C₃
prime radical	C₃×C₁₉×D₇₃	C₃
cosocle	C₃×C₇₃	C₂×C₃×C₁₉
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12483

Conjugacy classes & character table

6498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24966, 6);