#37573687

order	24448
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

C₁₉₁ ⋊ #2030

	subgroup	G/H
center	C₂²	#20259290
commutator, prime radical, cosocle	C₂⁴×C₁₉₁	C₂³
Frattini	C₂⁴	C₂²×D₁₉₁
Fitting	#381×C₁₉₁	C₂
socle	C₂²×C₁₉₁	#120
hypercenter	#381	D₁₉₁
hypocenter	C₁₉₁	#2030
LCS	G ▷ C₂⁴×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

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

μ_t(G) = 6112

Polycyclic presentation:

2^7,191|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^190

2686 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 5677);