Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C307 ⋊ C2 |
| Sylow | C307 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D307 |
| commutator, socle, cosocle | C22×C307 | C23 |
| Fitting | C2×Q8×C307 | C2 |
| prime radical | C2×D1228 | C2 |
| hypercenter | C2×Q8 | D307 |
| hypocenter | C307 | #124 |
| LCS | G ▷ C22×C307 ▷ C307 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^306,f^b=f^306,f^c=f^3061544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34087683, #34088060, #34088062, … |
| maximal normal subgroup of | #34087683, #34088060, #34088062, … |
| maximal quotient of | #34087752, #34087777, #34087788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 135);