Finite Group DatabasebetaFinite Group Databasebeta| order | 9488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C593 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14558631 |
| commutator, hypocenter | C593 | C2×C8 |
| Frattini | C2 | C2×#14558631 |
| Fitting | C4×C593 | C4 |
| socle | C2×C593 | C2×C4 |
| prime radical | C2×D593 | C4 |
| cosocle | Dic593 | C22 |
| LCS | G ▷ C593 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,593|a^2=c,c^2=d,e^a=e^77,e^b=e^592,e^c=e^592608 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14558631, #34039339, #34039347, … |
| maximal normal subgroup of | C8×#14558631, #34039339, #34039347, … |
| maximal quotient of | C4×#18011661, #34039342, #34039352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9488, 48);