#36442259

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Splittings

Sylow

C₈₉ ⋊ #7520

Subgroups

	subgroup	G/H
center	C₂	#26018397
commutator	C₄⋊Q₈×C₈₉	C₂×C₄
Frattini	#492	C₂×D₈₉
Fitting	C₈₉×#1623	C₂
socle	C₂×C₈₉	#1402
prime radical	#127×C₈₉	D₄
cosocle	#492×C₈₉	C₂²
hypercenter	#1623	D₈₉
hypocenter	C₈₉	#7520
LCS	G ▷ C₄⋊Q₈×C₈₉ ▷ C₄²×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #492 ◁ #1623

156 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 27 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) = 1424

Polycyclic presentation:

2^8,89|a^2=d,b^2=h,c^2=h,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^88,c^b=ch,d^b=deg,e^b=egh,f^b=fgh,d^c=dfg,e^c=egh,f^c=fh,e^d=egh,f^d=fh

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 57399);