Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C307 ⋊ C2 |
| Sylow | C307 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D307 |
| commutator, socle | C2×C307 | C2×C8 |
| Fitting | C16×C307 | C2 |
| prime radical | C2×D307 | C8 |
| cosocle | C8×C307 | C22 |
| hypercenter | C16 | D307 |
| hypocenter | C307 | M32 |
| LCS | G ▷ C2×C307 ▷ C307 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^3062468 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M32×D307, C2×#23754199, #34088303, … |
| maximal normal subgroup of | M32×D307, C2×#23754199, #34088303, … |
| maximal quotient of | #34087662, (C2×D307)⋊C16, Dic307⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 85);