#25014593

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

Splittings

Sylow

C₄₃ ⋊ #13158

Subgroups

	subgroup	G/H
center	C₂	#19135295
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1978	C₂
socle	C₂×C₄₃	#1936
prime radical	C₂²×D₈×C₄₃	C₂²
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1978	D₄₃
hypocenter	C₄₃	#13158
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #405 ◁ #1978

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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|a^2=f,b^2=dfgh,c^2=d,d^2=g,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,g^a=gh,i^a=i^42,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^42,e^c=eh,f^c=fh,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, 87564);