#36457392

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

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#19151506
commutator, prime radical, cosocle	C₂⁵×C₈₉	C₂³
Frattini	C₂⁵	C₂²×D₈₉
Fitting	C₈₉×#2483	C₂
socle	C₂²×C₈₉	#392
hypercenter	#2483	D₈₉
hypocenter	C₈₉	#10339
LCS	G ▷ C₂⁵×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2483

738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 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=g,b^2=g,c^2=h,b^a=bd,c^a=ce,f^a=fgh,c^b=cf,e^b=eh,d^c=dg,i^c=i^88

1706 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 72532);