Finite Group Databasebeta

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C₉×C₁₆×C₉₇ #72192161

order	13968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄×C₃₂ (order 4608) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄×C₃₂
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₃₉₆₈
abelian	C₉×C₁₆×C₉₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₈	C₂×C₃×C₉₇
socle, prime radical	C₂×C₃×C₉₇	C₃×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13968 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₃₉₆₈, D₂₇₉₃₆
Fitting subgroup of	D₁₃₉₆₈, Dic₆₉₈₄
maximal subgroup of	C₉×C₃₂×C₉₇, C₂×C₉×C₁₆×C₉₇, D₁₃₉₆₈, …
maximal normal subgroup of	C₉×C₃₂×C₉₇, C₂×C₉×C₁₆×C₉₇, D₁₃₉₆₈, …
maximal quotient of	C₉×C₃₂×C₉₇, C₂×C₉×C₁₆×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.