C₂²×C₃×C₅×C₁₃×C₁₃⋊C₃ #44478334

order	30420
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₅×C₁₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃×C₅×C₁₃×C₁₃⋊C₃

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

320 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

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

μ_t(G) = 2340

5460 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 923);