D₁₅⋊D₂₃ #13063417

order	1380
isoclinism	isoclinic class of D₁₅⋊D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₁₅⋊D₂₃
unambiguous semidirect product	D₆₉⋊D₅
unambiguous semidirect product	D₁₁₅⋊D₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₂₃	C₂²
LCS	G ▷ C₃×C₅×C₂₃
UCS	C₁

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 345

Polycyclic presentation:

2^2,3,5,23|d^a=d^4,e^a=e^22,c^b=c^2,d^b=d^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1380, 20);