#34046600

order	19072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₁₄₉ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₄₉
commutator, socle, prime radical	C₂²×C₁₄₉	C₂²×C₈
Fitting	C₈×Q₈×C₁₄₉	C₂
cosocle	C₂×C₈×C₁₄₉	C₂³
hypercenter	C₈×Q₈	D₁₄₉
hypocenter	C₁₄₉	#2183
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

126 conjugacy classes of subgroups.

μ_t(G) = 19072

Polycyclic presentation:

2^7,149|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^148,h^c=h^148

3016 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 6419);