C₈₂₇⋊C₃₂ #40996396

order	26464
automorphism	?
homology	Abelianization (H₁) = C₃₂ · Schur multiplier (H₂) = C₁

Aliases

C₈₂₇⋊C₃₂

C₈₂₇ ⋊ C₃₂

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₈₂₇
commutator, hypocenter	C₈₂₇	C₃₂
Fitting, cosocle	C₁₆×C₈₂₇	C₂
socle, prime radical	C₂×C₈₂₇	C₁₆
LCS	G ▷ C₈₂₇
UCS	C₁ ◁ C₁₆

12 conjugacy classes of subgroups.

μ_t(G) = 26464

Polycyclic presentation:

2^5,827|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^826

6640 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26464, 52);