Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C307 ⋊ C2 |
| Sylow | C307 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D307 |
| commutator, socle | C2×C307 | C22×C4 |
| Fitting | M16×C307 | C2 |
| prime radical | #19096826 | C2 |
| cosocle | C4×C307 | C23 |
| hypercenter | M16 | D307 |
| hypocenter | C307 | #131 |
| LCS | G ▷ C2×C307 ▷ C307 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=d,d^2=e,f^a=f^306,c^b=ce,f^c=f^3061550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34088001, #34088003, #34088006, … |
| maximal normal subgroup of | #34088001, #34088003, #34088006, … |
| maximal quotient of | #34087844, #34087845, #34087852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 154);