#37526571

order	22976
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₃₅₉ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₅₉
commutator, socle, prime radical	C₂²×C₃₅₉	C₂²×C₄
Fitting	#97×C₃₅₉	C₂
cosocle	C₂×C₄×C₃₅₉	C₂³
hypercenter	#97	D₃₅₉
hypocenter	C₃₅₉	#446
LCS	G ▷ C₂²×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #97

94 conjugacy classes of subgroups.

μ_t(G) = 22976

Polycyclic presentation:

2^6,359|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^358

3608 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 677);