Finite Group Databasebeta

← Prev (#72189693) Next (#72189695) →

C₂⁴×C₄×C₅²×C₇ #72189694

order	11200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 29727129600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₅

Aliases

abelian	C₂⁴×C₄×C₅²×C₇
multiplicative	(ℤ/31240)ˣ, (ℤ/37488)ˣ, (ℤ/42600)ˣ, (ℤ/46860)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁵×C₅²×C₇
socle, prime radical	C₂⁵×C₅²×C₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

10896 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₅²×C₇×C₈, C₂³×C₄²×C₅²×C₇, C₂⁵×C₄×C₅²×C₇
maximal normal subgroup of	C₂⁴×C₅²×C₇×C₈, C₂³×C₄²×C₅²×C₇, C₂⁵×C₄×C₅²×C₇
maximal quotient of	C₂⁴×C₅²×C₇×C₈, C₂³×C₄²×C₅²×C₇, C₂⁵×C₄×C₅²×C₇
automorphism group of	C₅×C₈×C₁₁×C₇₁
outer automorphism group of	C₅×C₈×C₁₁×C₇₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.