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C₈×C₂₇×C₄₇ #72188773

order	10152
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₉×C₂₃ (order 3312) · Inn(G) = C₁ · Out(G) = C₂⁴×C₉×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₁₅₂
abelian	C₈×C₂₇×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₄₇
socle, prime radical	C₂×C₃×C₄₇	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10152 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₁₅₂, D₂₀₃₀₄
maximal subgroup of	C₁₆×C₂₇×C₄₇, C₂×C₈×C₂₇×C₄₇, C₈×C₄₇×C₈₁, …
maximal normal subgroup of	C₁₆×C₂₇×C₄₇, C₂×C₈×C₂₇×C₄₇, C₈×C₄₇×C₈₁, …
maximal quotient of	C₁₆×C₂₇×C₄₇, C₂×C₈×C₂₇×C₄₇, C₈×C₄₇×C₈₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.