Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C307 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D307 |
| commutator, socle, prime radical, cosocle | C22×C307 | C23 |
| Fitting | C2×Q8×C307 | C2 |
| hypercenter | C2×Q8 | D307 |
| hypocenter | C307 | C4⋊Q8 |
| LCS | G ▷ C22×C307 ▷ C307 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^3061544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34087685, #34088068, #34088070, … |
| maximal normal subgroup of | #34087685, #34088068, #34088070, … |
| maximal quotient of | #34087756, #34087782, #34087792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 144);