Finite Group Databasebeta

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C₃×C₈×C₁₉×C₆₇ #72207331

order	30552
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁵×C₃×C₉×C₁₁ (order 9504) · Inn(G) = C₁ · Out(G) = C₂⁵×C₃×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₀₅₅₂
abelian	C₃×C₈×C₁₉×C₆₇
multiplicative	(ℤ/30553)ˣ, (ℤ/61106)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₉×C₆₇
socle, prime radical	C₂×C₃×C₁₉×C₆₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

30552 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₂₇₆, D₃₀₅₅₂
maximal subgroup of	Dic₁₅₂₇₆, D₃₀₅₅₂
maximal normal subgroup of	Dic₁₅₂₇₆, D₃₀₅₅₂
automorphism group of	C₃₀₅₅₃
outer automorphism group of	C₃₀₅₅₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.