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C₇₉×D₁₃⋊C₉ #32914860

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

Aliases

direct product	C₇₉×D₁₃⋊C₉
unambiguous semidirect product	D₁₃⋊(C₉×C₇₉)
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₂×C₇₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₂×C₉×C₇₉
Hall	C₇₉×C₁₃⋊C₉ ⋊ C₂
Hall	D₁₃×C₇₉ ⋊ C₉
Hall	C₁₃×C₇₉ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₂×C₇₉
Hall	D₁₃ ⋊ C₉×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂×C₉×C₇₉
Frattini	C₃	D₁₃⋊C₃×C₇₉
Fitting, socle	C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₃×D₁₃×C₇₉	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₇₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9243

Conjugacy classes & character table

1896 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₉×#261⋊C₉, #49149398, D₇₉×D₁₃⋊C₉, …
maximal normal subgroup of	C₇₉×#261⋊C₉, #49149398, D₇₉×D₁₃⋊C₉, …
maximal quotient of	C₇₉×Dic₁₃⋊C₉, C₂×C₇₉×D₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 23);