#36444865

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

C₈₉ ⋊ #8136

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂×C₄²
Fitting	C₄×#97×C₈₉	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×#97	D₈₉
hypocenter	C₈₉	#8136
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

478 conjugacy classes of subgroups.

μ_t(G) = 22784

Polycyclic presentation:

2^8,89|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=cg,c^b=ch,i^b=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, 60005);