Finite Group Databasebeta

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C₂×C₉×D₄₁₃ #28415501

order	14868
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₄₁₃
unambiguous semidirect product	(C₂×C₅₉)⋊(C₉×D₇)

Splittings

Fitting	C₂×C₇×C₉×C₅₉ ⋊ C₂
derived, Hall	C₇×C₅₉ ⋊ C₂²×C₉
Hall	C₇×C₉×C₅₉ ⋊ C₂²
Hall	C₉×C₅₉ ⋊ C₂×D₇
Hall	C₇×C₉ ⋊ C₂×D₅₉
Sylow	C₅₉ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×C₉×D₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₄₁₃
commutator, hypocenter	C₇×C₅₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₄₁₃
Fitting	C₂×C₇×C₉×C₅₉	C₂
socle	C₂×C₃×C₇×C₅₉	C₂×C₃
prime radical	C₂×C₃×D₄₁₃	C₃
cosocle	C₃×C₇×C₅₉	C₂²×C₃
LCS	G ▷ C₇×C₅₉
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7434

Conjugacy classes & character table

3744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14868, 30);