#30656866

order	16448
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₅₇ ⋊ #446

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₅₇
commutator, socle, prime radical	C₂²×C₂₅₇	C₂²×C₄
Fitting	C₄⋊C₈×C₂₅₇	C₂
cosocle	C₂×C₄×C₂₅₇	C₂³
hypercenter	C₄⋊C₈	D₂₅₇
hypocenter	C₂₅₇	#446
LCS	G ▷ C₂²×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

94 conjugacy classes of subgroups.

μ_t(G) = 16448

Polycyclic presentation:

2^6,257|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^b=g^256,g^c=g^256

2588 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 678);