C₂²⋊Dic₁₉ #64529

order	304
isoclinism	isoclinic class of Dic₃₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₂²⋊Dic₁₉

C₁₉ ⋊ C₂²⋊C₄

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 152

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(25,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,22,23)(24,25)(26,27)

Polycyclic presentation:

2^4,19|a^2=c,b^a=bd,e^a=e^18

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(304, 18);