Finite Group Databasebeta

← Prev (#72186361) Next (#72186363) →

C₂×C₃³×C₈×C₁₇ #72186362

order	7344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2875392
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×C₃³×C₈×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃³×C₁₇
socle, prime radical	C₂²×C₃³×C₁₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7344 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃³×C₁₆×C₁₇, C₃³×C₄×C₈×C₁₇, C₂²×C₃³×C₈×C₁₇, …
maximal normal subgroup of	C₂×C₃³×C₁₆×C₁₇, C₃³×C₄×C₈×C₁₇, C₂²×C₃³×C₈×C₁₇, …
maximal quotient of	C₂×C₃³×C₁₆×C₁₇, C₃³×C₄×C₈×C₁₇, C₂²×C₃³×C₈×C₁₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.