Finite Group DatabasebetaFinite Group Databasebeta| order | 9952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic311 |
| Sylow | C311 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D311 |
| commutator | C2×C311 | C22×C4 |
| Fitting, prime radical | C2×D4×C311 | C2 |
| socle, cosocle | C22×C311 | C23 |
| hypercenter | C2×D4 | D311 |
| hypocenter | C311 | C4×D4 |
| LCS | G ▷ C2×C311 ▷ C311 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
1570 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34091774, D8×Dic311, SD16×Dic311, … |
| maximal normal subgroup of | #34091774, D8×Dic311, SD16×Dic311, … |
| maximal quotient of | C22⋊C4×Dic311, C4⋊C4×Dic311, #34091569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9952, 109);