C₂²×C₃×C₅×((C₃⋊D₃)⋊C₃)⋊C₂ #72219448

order	6480
isoclinism	isoclinic class of ((C₃⋊D₃)⋊C₃)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₅ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₅	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂⁴×C₃×C₅
Frattini	C₃	C₂²×C₃×C₅×D₃²
Fitting	C₂²×C₃×C₅×H(3,𝔽₃)	C₂²
socle	C₂²×C₃²×C₅	D₃²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃×C₅

2386 conjugacy classes of subgroups; only the 436 normal subgroups are shown.

normal subgroups only

This group has 2386 conjugacy classes of subgroups — too many to draw. Only its 436 normal subgroups are shown.

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

660 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id.