ΓL(1,𝔽₈)⋊Dic₄₅₅ #50303650

order	38220
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₉₁)
commutator, hypocenter	C₅×C₇²×C₁₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₅×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₅×C₇×C₁₃×ΓL(1,𝔽₈)	C₂
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁ ◁ C₂

120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 5460

Polycyclic presentation:

2,3,5,7^2,13,2|a^2=g,c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^12,d^b=d^2

2284 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 336);