C₅×C₁₃⋊C₃×C₂²⋊(C₁₃⋊C₃) #44478140

order	30420
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₅×C₁₃⋊C₃×C₂²⋊(C₁₃⋊C₃)
unambiguous semidirect product	(C₂²×C₁₃⋊C₃)⋊(C₅×C₁₃⋊C₃)
unambiguous semidirect product	(C₁₃×C₁₃⋊C₃)⋊(C₅×A₄)
unambiguous semidirect product	(C₂²×C₅×C₁₃⋊C₃)⋊(C₁₃⋊C₃)
unambiguous semidirect product	(C₅×C₁₃×C₁₃⋊C₃)⋊A₄

	subgroup	G/H
center, hypercenter	C₅	C₁₃⋊C₃×C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃²	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₃²	C₃²
LCS	G ▷ C₂²×C₁₃²
UCS	C₁ ◁ C₅

152 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 780

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 729);