Finite Group DatabasebetaFinite Group Databasebeta| order | 9488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C593 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14558631 |
| commutator, socle | C2×C593 | C2×C4 |
| Fitting | C4×C593 | C4 |
| prime radical | C2×D593 | C4 |
| cosocle | Dic593 | C22 |
| hypercenter | C4 | #14558631 |
| hypocenter | C593 | M16 |
| LCS | G ▷ C2×C593 ▷ C593 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,593|a^2=c,c^2=d,b^a=bd,e^a=e^77,e^b=e^592,e^c=e^592602 conjugacy classes — view the full character table.
| maximal subgroup of | #34039349, #34039350, #34039355, … |
| maximal normal subgroup of | #34039349, #34039350, #34039355, … |
| maximal quotient of | #34039340, #34039342, C4⋊#18011661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9488, 50);