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C₇×C₉×C₁₃² #24922390

order	10647
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 943488
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₃

Aliases

C₇×C₉×C₁₃²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₇×C₁₃²
socle, prime radical	C₃×C₇×C₁₃²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10647 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	C₇⋊(C₉⋊(C₁₃⋊D₁₃))
Fitting subgroup of	C₇×C₉×C₁₃×D₁₃, C₇×C₉×C₁₃⋊D₁₃, C₉×C₁₃²×D₇, …
maximal subgroup of	C₂×C₇×C₉×C₁₃², C₇×C₉×C₁₃×D₁₃, C₇×C₉×C₁₃⋊D₁₃, …
maximal normal subgroup of	C₂×C₇×C₉×C₁₃², C₇×C₉×C₁₃×D₁₃, C₇×C₉×C₁₃⋊D₁₃, …
maximal quotient of	C₂×C₇×C₉×C₁₃², C₇×C₁₃²×C₂₇, C₃×C₇×C₉×C₁₃²

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 12);