Finite Group DatabasebetaFinite Group Databasebeta| order | 9952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×D4×C311 ⋊ C2 |
| Sylow | C311 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D311 |
| commutator, socle, cosocle | C22×C311 | C23 |
| Fitting | C2×D4×C311 | C2 |
| hypercenter | C2×D4 | D311 |
| hypocenter | C311 | #127 |
| LCS | G ▷ C22×C311 ▷ C311 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,311|b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^3101564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34091486, #34091860, #34091862, … |
| maximal normal subgroup of | #34091486, #34091860, #34091862, … |
| maximal quotient of | #34091563, #34091594, #34091595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9952, 142);