#36445568

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂×C₄

Aliases

No aliases for this group.

C₈₉ ⋊ #8263

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1273	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#8263
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

470 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 199 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=e,b^2=f,c^2=de,e^2=g,f^2=h,b^a=bd,c^a=cg,c^b=ch,i^b=i^88,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, 60708);