C₃²×D₃×#1020 #72220610

order	5184
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₃²×D₃×#1020

Fitting, socle	C₂⁴×C₃³ ⋊ C₂×D₃
derived	C₃×C₂²⋊A₄ ⋊ C₂²×C₃²

	subgroup	G/H
center, hypercenter	C₃²	D₃×#1020
commutator, cosocle, hypocenter	C₃×C₂²⋊A₄	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃³	C₂×D₃
LCS	G ▷ C₃×C₂²⋊A₄
UCS	C₁ ◁ C₃²

3790 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 3790 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

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

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

maximal subgroup of	D₃×C₃⋊D₃×#1020, C₃×D₃×#10593244
maximal normal subgroup of	D₃×C₃⋊D₃×#1020, C₃×D₃×#10593244

Past the SmallGroups library coverage — no SmallGroups id.