#25016007

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting	C₂×C₄₃×#362 ⋊ C₂
Sylow	C₄₃ ⋊ #13418

Subgroups

	subgroup	G/H
center	C₂	#19135828
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#362	C₂
socle	C₂×C₄₃	#2041
prime radical	C₂×#13063347	C₂²
hypercenter	C₂×#362	D₄₃
hypocenter	C₄₃	#13418
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#362

422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

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

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,43|b^2=h,c^2=d,d^2=h,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fg,g^a=gh,i^a=i^42,c^b=cf,d^b=dh,e^b=eg,f^b=fgh,g^b=gh,e^c=egh,f^c=fg,g^c=gh,i^c=i^42

Conjugacy classes & character table

706 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 88978);