#36441978

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

Aliases

No aliases for this group.

Fitting	C₈₉×#1324 ⋊ C₂
Sylow	C₈₉ ⋊ #7416

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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=d,c^2=f,d^2=g,e^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^88,c^b=cf,d^b=defh,e^b=eh,g^b=gh,i^b=i^88,d^c=dgh,e^c=eh

1175 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 57118);