Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C307⋊C32 |
| derived, Sylow | C307 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D307 |
| commutator, hypocenter | C307 | C32 |
| Fitting, cosocle | C16×C307 | C2 |
| socle, prime radical | C2×C307 | C16 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^3062480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D307, C2×C307⋊C32, #34087720, … |
| maximal normal subgroup of | C32×D307, C2×C307⋊C32, #34087720, … |
| maximal quotient of | C307⋊C64, C2×C307⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 52);