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C₃³×C₁₆×C₁₇ #72186359

order	7344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1437696
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₁₆×C₁₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃³×C₁₇
socle, prime radical	C₂×C₃³×C₁₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

280 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	C₃³×C₁₇×C₃₂, C₂×C₃³×C₁₆×C₁₇, C₃²×C₉×C₁₆×C₁₇, …
maximal normal subgroup of	C₃³×C₁₇×C₃₂, C₂×C₃³×C₁₆×C₁₇, C₃²×C₉×C₁₆×C₁₇, …
maximal quotient of	C₃³×C₁₇×C₃₂, C₂×C₃³×C₁₆×C₁₇, C₃²×C₉×C₁₆×C₁₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.