#36457691

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#19151510
commutator, prime radical, cosocle	C₂⁵×C₈₉	C₂³
Frattini	C₂⁵	C₂²×D₈₉
Fitting	C₈₉×#1819	C₂
socle	C₂²×C₈₉	#393
hypercenter	#1819	D₈₉
hypocenter	C₈₉	#10393
LCS	G ▷ C₂⁵×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #1819

526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

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

μ_t(G) = 2848

Polycyclic presentation:

2^8,89|a^2=dg,b^2=d,c^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fgh,i^a=i^88,c^b=cf,e^b=eh,f^b=fg,d^c=dg

1436 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 72831);