Finite Group Databasebeta

← Prev (#72183298) Next (#72183300) →

C₃×C₈×C₉×C₁₇ #72183299

order	3672
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₈×C₉×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃²×C₁₇
socle, prime radical	C₂×C₃²×C₁₇	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3672 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₉×C₁₆×C₁₇, C₂×C₃×C₈×C₉×C₁₇, C₃×C₈×C₁₇×C₂₇, …
maximal normal subgroup of	C₃×C₉×C₁₆×C₁₇, C₂×C₃×C₈×C₉×C₁₇, C₃×C₈×C₁₇×C₂₇, …
maximal quotient of	C₃×C₉×C₁₆×C₁₇, C₂×C₃×C₈×C₉×C₁₇, C₃×C₈×C₁₇×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.