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C₉×D₇×D₁₀₁ #38764128

order	25452
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₉×D₇×D₁₀₁

Splittings

Fitting, Hall	C₇×C₉×C₁₀₁ ⋊ C₂²
derived, Hall	C₇×C₁₀₁ ⋊ C₂²×C₉
Hall	C₉×C₁₀₁ ⋊ C₂×D₇
Sylow	C₁₀₁ ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×D₁₀₁
Sylow	C₇ ⋊ C₂×C₉×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₇×D₁₀₁
commutator, hypocenter	C₇×C₁₀₁	C₂²×C₉
Frattini	C₃	C₃×D₇×D₁₀₁
Fitting	C₇×C₉×C₁₀₁	C₂²
socle, cosocle	C₃×C₇×C₁₀₁	C₂²×C₃
prime radical	C₃×D₇×D₁₀₁	C₃
LCS	G ▷ C₇×C₁₀₁
UCS	C₁ ◁ C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6363

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25452, 22);