Finite Group Databasebeta

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C₃×C₈×C₁₇×C₃₇ #72193141

order	15096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₄×C₉×C₁₆ (order 4608) · Inn(G) = C₁ · Out(G) = C₂³×C₄×C₉×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₀₉₆
abelian	C₃×C₈×C₁₇×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₇×C₃₇
socle, prime radical	C₂×C₃×C₁₇×C₃₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15096 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₀₉₆, D₃₀₁₉₂
Fitting subgroup of	D₁₅₀₉₆, Dic₇₅₄₈
maximal subgroup of	C₃×C₁₆×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇, D₁₅₀₉₆, …
maximal normal subgroup of	C₃×C₁₆×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇, D₁₅₀₉₆, …
maximal quotient of	C₃×C₁₆×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.