Q₈×#127×C₈₉ #36414405

order	22784
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈₉ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

Q₈×#127×C₈₉

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#127×C₈₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

3498 conjugacy classes of subgroups.

μ_t(G) = 11392

6230 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 29545);