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C₇×C₈×C₁₉×C₂₇ #72205686

order	28728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁵×C₃×C₉² (order 7776) · Inn(G) = C₁ · Out(G) = C₂⁵×C₃×C₉²
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₈₇₂₈
abelian	C₇×C₈×C₁₉×C₂₇
multiplicative	(ℤ/28729)ˣ, (ℤ/57458)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₉	C₂×C₃×C₇×C₁₉
socle, prime radical	C₂×C₃×C₇×C₁₉	C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

28728 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₄₃₆₄, D₂₈₇₂₈
maximal subgroup of	Dic₁₄₃₆₄, D₂₈₇₂₈
maximal normal subgroup of	Dic₁₄₃₆₄, D₂₈₇₂₈
automorphism group of	C₂₈₇₂₉
outer automorphism group of	C₂₈₇₂₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.