C₇×D₅×(C₁₃⋊C₃)⋊D₇ #50304085

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₅×(C₁₃⋊C₃)⋊D₇
unambiguous semidirect product	(D₅×C₁₃⋊C₃)⋊(C₇×D₇)

	subgroup	G/H
center, hypercenter	C₇	D₅×(C₁₃⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₅×C₇×C₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₇

208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 910

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 771);