#44509354

order	30848
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₄₁ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₄₁
commutator, socle, prime radical	C₂²×C₂₄₁	C₂²×C₈
Fitting	C₈×Q₈×C₂₄₁	C₂
cosocle	C₂×C₈×C₂₄₁	C₂³
hypercenter	C₈×Q₈	D₂₄₁
hypocenter	C₂₄₁	#2183
LCS	G ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

126 conjugacy classes of subgroups.

μ_t(G) = 30848

Polycyclic presentation:

2^7,241|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^240,h^c=h^240

4856 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6419);