#28416563

order	14912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₃₃ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃₃
commutator, socle, prime radical	C₂²×C₂₃₃	C₂²×C₄
Fitting	#97×C₂₃₃	C₂
cosocle	C₂×C₄×C₂₃₃	C₂³
hypercenter	#97	D₂₃₃
hypocenter	C₂₃₃	#446
LCS	G ▷ C₂²×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

94 conjugacy classes of subgroups.

μ_t(G) = 14912

Polycyclic presentation:

2^6,233|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^232

2348 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 677);