Finite Group Databasebeta

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C₂×(C₇⋊C₉)⋊D₁₀₁ #38764124

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

Aliases

direct product	C₂×(C₇⋊C₉)⋊D₁₀₁
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊D₁₀₁
unambiguous semidirect product	(C₂×C₁₀₁)⋊(D₇⋊C₉)
unambiguous semidirect product	(C₂×D₇₀₇)⋊C₉

Splittings

derived, Hall	C₇×C₁₀₁ ⋊ C₂²×C₉
Hall	C₇⋊C₉×C₁₀₁ ⋊ C₂²
Hall	C₂×D₇₀₇ ⋊ C₉
Sylow	C₁₀₁ ⋊ C₂×D₇⋊C₉
Hall	C₇⋊C₉ ⋊ C₂×D₁₀₁
Sylow	C₇ ⋊ C₂×C₉×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₀₁
commutator, hypocenter	C₇×C₁₀₁	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₀₁
Fitting, socle	C₂×C₃×C₇×C₁₀₁	C₂×C₃
prime radical	C₂×C₃×D₇₀₇	C₃
cosocle	C₃×C₇×C₁₀₁	C₂²×C₃
LCS	G ▷ C₇×C₁₀₁
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12726

Conjugacy classes & character table

1542 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25452, 18);