C₂×C₃×C₃⋊(C₅⋊(C₁₃⋊D₁₃)) #44478347

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₁₃

Aliases

direct product	C₂×C₃×C₃⋊(C₅⋊(C₁₃⋊D₁₃))
unambiguous semidirect product	(C₂×C₃)⋊(C₃×C₅⋊(C₁₃⋊D₁₃))
unambiguous semidirect product	(C₂×C₅)⋊(C₃×C₃⋊(C₁₃⋊D₁₃))

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₅⋊(C₁₃⋊D₁₃))
commutator, cosocle, hypocenter	C₃×C₅×C₁₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₃²	C₂
LCS	G ▷ C₃×C₅×C₁₃²
UCS	C₁ ◁ C₂×C₃

704 conjugacy classes of subgroups; only the 262 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 262 normal subgroups are shown.

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

μ_t(G) = 10140

7614 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 936);