Finite Group DatabasebetaFinite Group Databasebeta| order | 9952 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C22⋊D311 |
| Fitting | C24×C311 ⋊ C2 |
| Sylow | C311 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D311 |
| commutator, cosocle | C2×C311 | C24 |
| Frattini | C2 | C23×D311 |
| Fitting | C24×C311 | C2 |
| socle | C23×C311 | C22 |
| hypercenter | C24 | D311 |
| hypocenter | C311 | C22×D4 |
| LCS | G ▷ C2×C311 ▷ C311 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
2500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34091570, #34091571, #34091573, … |
| maximal normal subgroup of | #34091570, #34091571, #34091573, … |
| maximal quotient of | C22×(C2×D311)⋊C4, C22×C22⋊Dic311, C22×Dic311⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9952, 183);