Finite Group Databasebeta

← Prev (#32914840) Next (#32914842) →

C₂×C₇₉×C₁₃⋊C₉ #32914841

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇₉×C₁₃⋊C₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₉×C₇₉)

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18486

Conjugacy classes & character table

3318 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 4);