#31808310

order	17792
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₃₉ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₃₉
commutator, socle, prime radical	C₂²×C₁₃₉	C₂²×C₈
Fitting	#346×C₁₃₉	C₂
cosocle	C₂×C₈×C₁₃₉	C₂³
hypercenter	#346	D₁₃₉
hypocenter	C₁₃₉	#2183
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₈ ◁ #346

126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

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

μ_t(G) = 17792

Polycyclic presentation:

2^7,139|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^b=h^138

2816 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 6416);