C₁₂₇×#15510 #44579183

order	32512
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₂₇ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₂₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₂₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₂₇ ◁ G

1478 conjugacy classes of subgroups.

μ_t(G) = 32512

7366 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32512, 8498);