C₇×D₆₅⋊(C₃⋊D₃) #30655701

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₇×D₆₅⋊(C₃⋊D₃)
unambiguous semidirect product	D₆₅⋊(C₇×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₇	D₆₅⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃²×C₅×C₁₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₂²
LCS	G ▷ C₃²×C₅×C₁₃
UCS	C₁ ◁ C₇

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

normal subgroups only

This group has 240 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) = 4095

1176 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 751);