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C₂²×C₃×C₈₆₃ #23780450

order	10356
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10344
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₈₆₃
multiplicative	(ℤ/15537)ˣ, (ℤ/20716)ˣ, (ℤ/31074)ˣ

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10356 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²⋊C₉×C₈₆₃, C₃×A₄×C₈₆₃
socle of	C₂²×C₉×C₈₆₃, C₂²⋊C₉×C₈₆₃, C₃×A₄×C₈₆₃
maximal subgroup of	C₂²×C₉×C₈₆₃, C₂²⋊C₉×C₈₆₃, C₂²×C₃²×C₈₆₃, …
maximal normal subgroup of	C₂²×C₉×C₈₆₃, C₂²⋊C₉×C₈₆₃, C₂²×C₃²×C₈₆₃, …
maximal quotient of	C₂²×C₉×C₈₆₃, C₂²×C₃²×C₈₆₃, C₂×C₃×D₃×C₈₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10356, 5);