#35323829

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#19127888
commutator, prime radical, cosocle	C₂²×D₄×C₈₃	C₂³
Frattini	C₂²×D₄	C₂²×D₈₃
Fitting	C₈₃×#2724	C₂
socle	C₂²×C₈₃	B(4,𝔽₂)
hypercenter	#2724	D₈₃
hypocenter	C₈₃	#13421
LCS	G ▷ C₂²×D₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ #2724

496 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 5312

Polycyclic presentation:

2^8,83|a^2=h,b^2=h,c^2=d,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,e^b=eg,g^c=gh,i^c=i^82,f^e=fh

1343 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 88993);