D₂₂₈ #90716

order	456
isoclinism	isoclinic class of Dic₁₁₄
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₂₈
unambiguous semidirect product	C₄⋊D₅₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 228

A minimal faithful permutation representation — 2 generators on 26 points:

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

Polycyclic presentation:

2^3,3,19|b^2=c,b^a=bc,d^a=d^2,e^a=e^18

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 36);