C₂⁴×D₃×D₅ #11757192

order	960
isoclinism	isoclinic class of D₃×D₅
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product	C₂⁴×D₃×D₅
unambiguous semidirect product	(C₅×D₃)⋊C₂⁵
unambiguous semidirect product	(C₃×D₅)⋊C₂⁵
unambiguous semidirect product	D₁₅⋊C₂⁵

	subgroup	G/H
center, hypercenter	C₂⁴	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁶
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴

11300 conjugacy classes of subgroups; only the 3640 normal subgroups are shown.

normal subgroups only

This group has 11300 conjugacy classes of subgroups — too many to draw. Only its 3640 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 240

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 11387);