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C₉×H(3,𝔽₃)×C₄₇ #26037697

order	11421
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉×C₄₇ · Schur multiplier (H₂) = C₃⁴

Aliases

C₉×H(3,𝔽₃)×C₄₇

Subgroups

	subgroup	G/H
center	C₃×C₉×C₄₇	C₃²
commutator	C₃	C₃²×C₉×C₄₇
Frattini, cosocle	C₃²	C₃³×C₄₇
socle	C₃²×C₄₇	C₃³
prime radical	C₃×H(3,𝔽₃)×C₄₇	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₇ ◁ G

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4653 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×H(3,𝔽₃)⋊C₂₇, C₄₇×#10624453, C₄₇×#10624583, …
maximal normal subgroup of	C₄₇×H(3,𝔽₃)⋊C₂₇, C₄₇×#10624453, C₄₇×#10624583, …
maximal quotient of	C₉×C₄₇×C₃²⋊C₉, C₄₇×#10624555, C₄₇×#10624556, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11421, 35);