Finite Group Databasebeta

← Prev (#72186403) Next (#72186405) →

C₈×C₂₅×C₃₇ #72186404

order	7400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄²×C₅×C₉ (order 2880) · Inn(G) = C₁ · Out(G) = C₂²×C₄²×C₅×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₄₀₀
abelian	C₈×C₂₅×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₅	C₂×C₅×C₃₇
socle, prime radical	C₂×C₅×C₃₇	C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7400 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₈₀₀, Dic₇₄₀₀
maximal subgroup of	C₁₆×C₂₅×C₃₇, C₂×C₈×C₂₅×C₃₇, C₃×C₈×C₂₅×C₃₇, …
maximal normal subgroup of	C₁₆×C₂₅×C₃₇, C₂×C₈×C₂₅×C₃₇, C₃×C₈×C₂₅×C₃₇, …
maximal quotient of	C₁₆×C₂₅×C₃₇, C₂×C₈×C₂₅×C₃₇, C₃×C₈×C₂₅×C₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.