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C₃×C₇×C₈×C₉₇ #72194235

order	16296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₃₂ (order 4608) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₃₂
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₂₉₆
abelian	C₃×C₇×C₈×C₉₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₇×C₉₇
socle, prime radical	C₂×C₃×C₇×C₉₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16296 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₂₉₆, D₃₂₅₉₂
Fitting subgroup of	Dic₈₁₄₈, D₁₆₂₉₆
maximal subgroup of	C₃×C₇×C₁₆×C₉₇, C₂×C₃×C₇×C₈×C₉₇, Dic₈₁₄₈, …
maximal normal subgroup of	C₃×C₇×C₁₆×C₉₇, C₂×C₃×C₇×C₈×C₉₇, Dic₈₁₄₈, …
maximal quotient of	C₃×C₇×C₁₆×C₉₇, C₂×C₃×C₇×C₈×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.