C₁₃×D₆₅⋊(C₃⋊D₃) #44478323

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

Aliases

direct product	C₁₃×D₆₅⋊(C₃⋊D₃)
unambiguous semidirect product	D₆₅⋊(C₁₃×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₆₅⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃²×C₅×C₁₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₂²
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₁₃

384 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 1170

2184 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 912);