Finite Group Databasebeta

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C₇×C₈×C₂₅₇ #72192534

order	14392
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₂₅₆ (order 6144) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₂₅₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₄₃₉₂
abelian	C₇×C₈×C₂₅₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₂₅₇
socle, prime radical	C₂×C₇×C₂₅₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14392 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₄₃₉₂, D₂₈₇₈₄
Fitting subgroup of	D₁₄₃₉₂, Dic₇₁₉₆
maximal subgroup of	C₇×C₁₆×C₂₅₇, C₂×C₇×C₈×C₂₅₇, D₁₄₃₉₂, …
maximal normal subgroup of	C₇×C₁₆×C₂₅₇, C₂×C₇×C₈×C₂₅₇, D₁₄₃₉₂, …
maximal quotient of	C₇×C₁₆×C₂₅₇, C₂×C₇×C₈×C₂₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.