C₄⋊(D₁₉⋊C₃) #90689

order	456
isoclinism	isoclinic class of (C₁₉⋊C₃)⋊Q₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₄⋊(D₁₉⋊C₃)
unambiguous semidirect product	D₇₆⋊C₃

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 76

A minimal faithful permutation representation — 2 generators on 23 points:

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

Polycyclic presentation:

2^2,3,2,19|b^2=d,b^a=bd,e^a=e^18,e^c=e^7

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 9);