Finite Group Databasebeta

← Prev (#72189125) Next (#72189127) →

C₂⁴×C₃²×C₇₃ #72189126

order	10512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 69672960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

abelian	C₂⁴×C₃²×C₇₃
multiplicative	(ℤ/24584)ˣ, (ℤ/31608)ˣ, (ℤ/36876)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃²×C₄×C₇₃, C₂⁵×C₃²×C₇₃, C₂⁴×C₃×C₉×C₇₃, …
maximal normal subgroup of	C₂³×C₃²×C₄×C₇₃, C₂⁵×C₃²×C₇₃, C₂⁴×C₃×C₉×C₇₃, …
maximal quotient of	C₂³×C₃²×C₄×C₇₃, C₂⁵×C₃²×C₇₃, C₂⁴×C₃×C₉×C₇₃, …
automorphism group of	C₇×C₈×C₄₃₉, C₈×C₉×C₄₃₉
outer automorphism group of	C₇×C₈×C₄₃₉, C₈×C₉×C₄₃₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.