Finite Group Databasebeta

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C₂×C₁₃×C₇₉⋊C₉ #32914840

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₂×C₁₃×C₇₉⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₂×C₉×C₁₃
Hall	C₂×C₁₃×C₇₉ ⋊ C₉
Hall	C₁₃×C₇₉ ⋊ C₂×C₉
Hall	C₂×C₇₉ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	C₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×C₇₉⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₇₉	C₃
cosocle	C₃×C₇₉	C₂×C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18486

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₁₃×C₇₉⋊C₉, C₁₃×Dic₇₉⋊C₉, Dic₁₃×C₇₉⋊C₉, …
maximal normal subgroup of	C₄×C₁₃×C₇₉⋊C₉, C₁₃×Dic₇₉⋊C₉, Dic₁₃×C₇₉⋊C₉, …
maximal quotient of	C₄×C₁₃×C₇₉⋊C₉, C₂²×C₁₃×C₇₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 3);