C₅×C₁₃×C₃⋊D₃×D₁₃ #44478294

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₅×C₁₃×C₃⋊D₃×D₁₃
unambiguous semidirect product	(C₃×D₁₃)⋊(C₅×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₃⋊D₃×D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅×C₁₃

384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

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

μ_t(G) = 1170

3120 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 883);