Finite Group Databasebeta

← Prev (#72186336) Next (#72186338) →

C₃×C₈×C₁₆×C₁₉ #72186337

order	7296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 73728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

abelian	C₃×C₈×C₁₆×C₁₉
multiplicative	(ℤ/7769)ˣ, (ℤ/15538)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₃×C₁₉
socle, prime radical	C₂²×C₃×C₁₉	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₈×C₁₉×C₃₂, C₃×C₁₆²×C₁₉, C₂×C₃×C₈×C₁₆×C₁₉, …
maximal normal subgroup of	C₃×C₈×C₁₉×C₃₂, C₃×C₁₆²×C₁₉, C₂×C₃×C₈×C₁₆×C₁₉, …
maximal quotient of	C₃×C₈×C₁₉×C₃₂, C₃×C₁₆²×C₁₉, C₂×C₃×C₈×C₁₆×C₁₉, …
automorphism group of	C₁₇×C₄₅₇
outer automorphism group of	C₁₇×C₄₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.