Finite Group Databasebeta

← Prev (#72187261) Next (#72187263) →

C₂²×C₈×C₉×C₂₉ #72187262

order	8352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 64512
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₈×C₉×C₂₉
multiplicative	(ℤ/12921)ˣ, (ℤ/13281)ˣ, (ℤ/16712)ˣ, (ℤ/16736)ˣ, (ℤ/17228)ˣ, (ℤ/17708)ˣ, (ℤ/25068)ˣ, (ℤ/25164)ˣ, (ℤ/25842)ˣ, (ℤ/26562)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂³×C₃×C₂₉
socle, prime radical	C₂³×C₃×C₂₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₉×C₁₆×C₂₉, C₂×C₄×C₈×C₉×C₂₉, C₂³×C₈×C₉×C₂₉, …
maximal normal subgroup of	C₂²×C₉×C₁₆×C₂₉, C₂×C₄×C₈×C₉×C₂₉, C₂³×C₈×C₉×C₂₉, …
maximal quotient of	C₂²×C₉×C₁₆×C₂₉, C₂×C₄×C₈×C₉×C₂₉, C₂³×C₈×C₉×C₂₉, …
automorphism group of	C₄×C₂₇×C₂₃₃
outer automorphism group of	C₄×C₂₇×C₂₃₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.