C₅×D₆₃⋊D₁₃ #30655130

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

Aliases

direct product	C₅×D₆₃⋊D₁₃
unambiguous semidirect product	D₆₃⋊(C₅×D₁₃)
unambiguous semidirect product	D₉₁⋊(C₅×D₉)
unambiguous semidirect product	D₁₁₇⋊(C₅×D₇)

	subgroup	G/H
center, hypercenter	C₅	D₆₃⋊D₁₃
commutator, cosocle, hypocenter	C₇×C₉×C₁₃	C₂²×C₅
Frattini	C₃	C₅×D₂₁⋊D₁₃
Fitting	C₅×C₇×C₉×C₁₃	C₂²
socle	C₃×C₅×C₇×C₁₃	C₂×D₃
LCS	G ▷ C₇×C₉×C₁₃
UCS	C₁ ◁ C₅

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

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

μ_t(G) = 4095

1140 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 180);