C₆₄₃⋊C₈ #19104113

order	5144
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

C₆₄₃⋊C₈

C₆₄₃ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₆₄₃
commutator, hypocenter	C₆₄₃	C₈
Fitting	C₄×C₆₄₃	C₂
socle	C₂×C₆₄₃	C₄
LCS	G ▷ C₆₄₃
UCS	C₁ ◁ C₄

8 conjugacy classes of subgroups.

Polycyclic presentation:

2^3,643|a^2=b,b^2=c,d^a=d^642

1292 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5144, 6);