C₃×C₅×D₇×D₁₃⋊C₃ #30655321

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₅×D₇×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃²×C₅×D₇)

	subgroup	G/H
center, hypercenter	C₃×C₅	D₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₅

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

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

μ_t(G) = 1365

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 371);