Dic₁₇₅₇ #20296346

order	7028
automorphism	Aut(G) order 5271000
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₁₇₅₇
unambiguous semidirect product	C₇⋊Dic₂₅₁
unambiguous semidirect product	C₂₅₁⋊Dic₇

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₇₅₇
commutator, hypocenter	C₇×C₂₅₁	C₄
Fitting, socle	C₂×C₇×C₂₅₁	C₂
LCS	G ▷ C₇×C₂₅₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Polycyclic presentation:

2,7,251,2|a^2=d,b^a=b^6,c^a=c^250

1760 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7028, 4);