#35321093

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting	C₈₃×#1953 ⋊ C₂
Sylow	C₈₃ ⋊ #12949

Subgroups

	subgroup	G/H
center	C₂	#24907723
commutator	C₂×C₈×C₈₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₃
Fitting	C₈₃×#1953	C₂
socle	C₂×C₈₃	#1864
prime radical	C₂×#14581814	C₂²
cosocle	C₂²×C₈×C₈₃	C₂³
hypercenter	#1953	D₈₃
hypocenter	C₈₃	#12949
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #405 ◁ #1953

394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2656

Polycyclic presentation:

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

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 86257);