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C₂×C₂₇×C₂₈₁ #72193196

order	15174
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₅×C₇×C₈×C₉ (order 5040) · Inn(G) = C₁ · Out(G) = C₂×C₅×C₇×C₈×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₁₇₄
abelian	C₂×C₂₇×C₂₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₂₈₁
socle, prime radical	C₂×C₃×C₂₈₁	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15174 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₁₇₄, D₃₀₃₄₈
Fitting subgroup of	C₂×D₇₅₈₇, Dic₇₅₈₇
maximal subgroup of	C₄×C₂₇×C₂₈₁, C₂²×C₂₇×C₂₈₁, C₂×D₇₅₈₇, …
maximal normal subgroup of	C₄×C₂₇×C₂₈₁, C₂²×C₂₇×C₂₈₁, C₂×D₇₅₈₇, …
maximal quotient of	C₄×C₂₇×C₂₈₁, C₂²×C₂₇×C₂₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.