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C₅₃₉₉ #19129227

order	5399
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₂₆₉₉ (order 5398) · Inn(G) = C₁ · Out(G) = C₂×C₂₆₉₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

C₅₃₉₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₁

2 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5399 conjugacy classes. The character table is too large to display.

Relationships

center of	D₃×C₅₃₉₉
derived subgroup of	Dic₅₃₉₉, C₂×D₅₃₉₉, C₃×D₅₃₉₉
maximal subgroup of	C₃×C₅₃₉₉, C₅×C₅₃₉₉, C₇×C₅₃₉₉
maximal normal subgroup of	C₃×C₅₃₉₉, C₅×C₅₃₉₉, C₇×C₅₃₉₉
maximal quotient of	C₃×C₅₃₉₉, C₅×C₅₃₉₉, C₇×C₅₃₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5399, 1);