Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #95×C151 ⋊ C2 |
| Sylow | C151 ⋊ #397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D151 |
| commutator, socle, cosocle | C23×C151 | C23 |
| Fitting | #95×C151 | C2 |
| prime radical | C23×D151 | C22 |
| hypercenter | #95 | D151 |
| hypocenter | C151 | #397 |
| LCS | G ▷ C23×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ #95 | |
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,151|a^2=e,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^150,g^c=g^1501522 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34068097, #34068102, #34068125, … |
| maximal normal subgroup of | #34068097, #34068102, #34068125, … |
| maximal quotient of | #34067356, #34067358, #34067367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 476);