#36361838

order	22144
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₇₃ ⋊ #2845

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₇₃
commutator, socle, prime radical, cosocle	C₂³×C₁₇₃	C₂⁴
Fitting	#382×C₁₇₃	C₂
hypercenter	#382	D₁₇₃
hypocenter	C₁₇₃	#2845
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ #382

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

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

μ_t(G) = 22144

Polycyclic presentation:

2^7,173|a^2=ef,b^2=g,c^2=eg,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^172

2434 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22144, 12785);