#25015518

order	11008
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Splittings

Fitting	C₄₃×#1379 ⋊ C₂
Sylow	C₄₃ ⋊ #13339

Subgroups

	subgroup	G/H
center	C₂²	#14583035
commutator, cosocle	C₂²×C₈×C₄₃	C₂³
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1379	C₂
socle	C₂²×C₄₃	#447
prime radical	C₂×#13063347	C₂²
hypercenter	#1379	D₄₃
hypocenter	C₄₃	#13339
LCS	G ▷ C₂²×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405 ◁ #1379

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

normal subgroups only

This group has 534 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

Polycyclic presentation:

2^8,43|a^2=h,b^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^42,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^42,d^c=dgh,e^c=eg,f^c=fh,g^c=gh,i^c=i^42

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 88489);