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(C₇₉⋊C₉)⋊C₉ #20264236

order	6399
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product

(C₇₉⋊C₉)⋊C₉

Splittings

C₇₉ ⋊ C₉⋊C₉

Subgroups

	subgroup	G/H
center, Frattini	C₃²	C₃×C₇₉⋊C₃
commutator	C₃×C₇₉	C₃×C₉
Fitting	C₃×C₉×C₇₉	C₃
socle	C₃²×C₇₉	C₃²
hypercenter	C₃×C₉	C₇₉⋊C₃
hypocenter	C₇₉	C₉⋊C₉
LCS	G ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃×C₉

34 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3^4,79|a^3=d,b^3=c,b^a=bc,e^b=e^23

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉⋊C₉×C₇₉⋊C₃, C₃×(C₇₉⋊C₉)⋊C₉, #34063234, …
maximal normal subgroup of	C₉⋊C₉×C₇₉⋊C₃, C₃×(C₇₉⋊C₉)⋊C₉, #34063234, …
maximal quotient of	C₇₉⋊#6855, (C₇₉⋊C₉)⋊C₂₇, #34063190, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6399, 20);