Finite Group Databasebeta

← Prev (#72185754) Next (#72185756) →

C₂⁵×C₉×C₂₃ #72185755

order	6624
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1319915520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁵×C₉×C₂₃
multiplicative	(ℤ/21432)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁵×C₃×C₂₃
socle, prime radical	C₂⁵×C₃×C₂₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

2244 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₉×C₂₃, C₂⁶×C₉×C₂₃, C₂⁵×C₂₃×C₂₇, …
maximal normal subgroup of	C₂⁴×C₄×C₉×C₂₃, C₂⁶×C₉×C₂₃, C₂⁵×C₂₃×C₂₇, …
maximal quotient of	C₂⁴×C₄×C₉×C₂₃, C₂⁶×C₉×C₂₃, C₂⁵×C₂₃×C₂₇, …
automorphism group of	C₃×C₈×C₁₉×C₄₇
outer automorphism group of	C₃×C₈×C₁₉×C₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.