Finite Group DatabasebetaFinite Group Databasebeta| order | 9952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C311 ⋊ C2 |
| Sylow | C311 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D311 |
| commutator, cosocle | C4×C311 | C23 |
| Frattini | C4 | C22×D311 |
| Fitting | Q16×C311 | C2 |
| socle | C2×C311 | C2×D4 |
| hypercenter | Q16 | D311 |
| hypocenter | C311 | #135 |
| LCS | G ▷ C4×C311 ▷ C2×C311 ▷ C311 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,311|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^310,d^b=de,f^b=f^310,f^c=f^3101099 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34092125, #34092127, #34092131, … |
| maximal normal subgroup of | #34092125, #34092127, #34092131, … |
| maximal quotient of | #34091689, #34091731, #34091776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9952, 169);