C₇₉⋊C₆₄ #19098282

order	5056
automorphism	?
homology	Abelianization (H₁) = C₆₄ · Schur multiplier (H₂) = C₁

Aliases

C₇₉⋊C₆₄

C₇₉ ⋊ C₆₄

	subgroup	G/H
center, Frattini, hypercenter	C₃₂	D₇₉
commutator, hypocenter	C₇₉	C₆₄
Fitting	C₃₂×C₇₉	C₂
socle	C₂×C₇₉	C₃₂
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃₂

14 conjugacy classes of subgroups.

Polycyclic presentation:

2^6,79|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^78

1312 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5056, 268);