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C₉×H(3,𝔽₃)×C₂₉ #20296453

order	7047
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₂₉ · Schur multiplier (H₂) = C₃⁴

Aliases

C₉×H(3,𝔽₃)×C₂₉

Subgroups

	subgroup	G/H
center	C₃×C₉×C₂₉	C₃²
commutator	C₃	C₃²×C₉×C₂₉
Frattini	C₃²	C₃³×C₂₉
socle	C₃²×C₂₉	C₃³
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₂₉ ◁ G

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×H(3,𝔽₃)⋊C₂₇, C₂₉×#10624453, C₂₉×#10624583, …
maximal normal subgroup of	C₂₉×H(3,𝔽₃)⋊C₂₇, C₂₉×#10624453, C₂₉×#10624583, …
maximal quotient of	C₉×C₂₉×C₃²⋊C₉, C₂₉×#10624555, C₂₉×#10624556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7047, 35);