Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C307⋊#95 |
| Sylow | C307 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D307 |
| commutator | C2×C307 | C42 |
| Fitting | C22×C4×C307 | C2 |
| socle, prime radical, cosocle | C23×C307 | C22 |
| hypercenter | C22×C4 | D307 |
| hypocenter | C307 | #95 |
| LCS | G ▷ C2×C307 ▷ C307 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=d,b^2=e,b^a=bc,f^b=f^3062468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34087621, #34087622, #34087624, … |
| maximal normal subgroup of | #34087621, #34087622, #34087624, … |
| maximal quotient of | #34087641, #34087642, #34087643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 53);