Dic₁₃₀₄ #19104682

order	5216
automorphism	Aut(G) order 3379968
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

Dic₁₃₀₄

C₁₆₃ ⋊ Q₃₂

24 conjugacy classes of subgroups.

Polycyclic presentation:

2^5,163|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^162,c^b=cd,d^b=de,f^b=f^162

1307 conjugacy classes. The character table is too large to display.

maximal subgroup of	Dic₃₉₁₂, Dic₆₅₂₀, Dic₉₁₂₈, …
maximal quotient of	Dic₃₉₁₂, Dic₆₅₂₀, Dic₉₁₂₈, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5216, 93);