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C₇×C₉×C₁₆² #72194091

order	16128
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 884736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

abelian	C₇×C₉×C₁₆²
multiplicative	(ℤ/17153)ˣ, (ℤ/34306)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈²	C₂²×C₃×C₇
socle, prime radical	C₂²×C₃×C₇	C₃×C₈²
LCS	G ▷ C₁
UCS	C₁ ◁ G

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16128 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×C₁₆×C₃₂, C₂×C₇×C₉×C₁₆²
maximal normal subgroup of	C₇×C₉×C₁₆×C₃₂, C₂×C₇×C₉×C₁₆²
maximal quotient of	C₇×C₉×C₁₆×C₃₂, C₂×C₇×C₉×C₁₆²
automorphism group of	C₁₇×C₁₀₀₉
outer automorphism group of	C₁₇×C₁₀₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.