C₅×D₃×ΓL(1,𝔽₈)×D₁₃ #30655411

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

Aliases

	subgroup	G/H
center, hypercenter	C₅	D₃×ΓL(1,𝔽₈)×D₁₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₅

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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, 461);