Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D307 |
| Fitting | C42×C307 ⋊ C2 |
| derived, Sylow | C307 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D307 |
| commutator, hypocenter | C307 | C2×C42 |
| Frattini | C22 | C22×D307 |
| Fitting | C42×C307 | C2 |
| socle, cosocle | C22×C307 | C23 |
| prime radical | C22×D307 | C22 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C42 | |
108 conjugacy classes of subgroups.
2480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×D307, #97×D307, C4×#19096809, … |
| maximal normal subgroup of | C4×C8×D307, #97×D307, C4×#19096809, … |
| maximal quotient of | C42×Dic307, #95×D307, #34087732, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 94);