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C₂²×C₃×C₈₈₇ #24922370

order	10644
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10632
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₈₈₇
multiplicative	(ℤ/15969)ˣ, (ℤ/21292)ˣ, (ℤ/31938)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

10644 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂²⋊C₉×C₈₈₇, C₃×A₄×C₈₈₇
socle of	C₂²×C₉×C₈₈₇, C₂²⋊C₉×C₈₈₇, C₃×A₄×C₈₈₇
maximal subgroup of	C₂²×C₉×C₈₈₇, C₂²⋊C₉×C₈₈₇, C₂²×C₃²×C₈₈₇, …
maximal normal subgroup of	C₂²×C₉×C₈₈₇, C₂²⋊C₉×C₈₈₇, C₂²×C₃²×C₈₈₇, …
maximal quotient of	C₂²×C₉×C₈₈₇, C₂²×C₃²×C₈₈₇, C₂×C₃×D₃×C₈₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10644, 5);