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C₈₉×#13815 #36391663

order	22784
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₈₉ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

C₈₉×#13815

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₈₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₈₉
Frattini, cosocle	C₂⁴	C₂⁴×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

1602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 22784

Conjugacy classes & character table

8900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 6803);