D₃×C₇×C₁₃×D₃₅ #50304459

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₇×C₁₃×D₃₅
unambiguous semidirect product	(C₅×D₃)⋊(C₇×C₁₃×D₇)
unambiguous semidirect product	(D₃×C₇)⋊(C₇×D₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₃×D₃₅
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₇×C₁₃

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

μ_t(G) = 2730

5187 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1145);