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C₇×C₈×C₁₉₃ #72189362

order	10808
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₆₄ (order 4608) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₈₀₈
abelian	C₇×C₈×C₁₉₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₉₃
socle, prime radical	C₂×C₇×C₁₉₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10808 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₈₀₈, D₂₁₆₁₆
maximal subgroup of	C₇×C₁₆×C₁₉₃, C₂×C₇×C₈×C₁₉₃, C₃×C₇×C₈×C₁₉₃, …
maximal normal subgroup of	C₇×C₁₆×C₁₉₃, C₂×C₇×C₈×C₁₉₃, C₃×C₇×C₈×C₁₉₃, …
maximal quotient of	C₇×C₁₆×C₁₉₃, C₂×C₇×C₈×C₁₉₃, C₃×C₇×C₈×C₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.