#36472053

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	#13105
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

314 conjugacy classes of subgroups.

μ_t(G) = 22784

Polycyclic presentation:

2^8,89|a^2=f,b^2=f,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^88,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, 87193);