#36470829

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂²×C₈
Fitting	C₈₉×#1374	C₂
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1374	D₈₉
hypocenter	C₈₉	#12895
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

298 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

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

μ_t(G) = 22784

Polycyclic presentation:

2^8,89|a^2=f,b^2=de,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^c=i^88

3608 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 85969);