Finite Group DatabasebetaFinite Group Databasebeta| order | 9488 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C593 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #18011663 |
| commutator, hypocenter | C593 | C16 |
| Fitting, socle, prime radical | C2×C593 | C8 |
| cosocle | #18011661 | C2 |
| LCS | G ▷ C593 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,593|a^2=b,b^2=c,c^2=d,e^a=e^392,e^b=e^77,e^c=e^592164 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23748745, #34039380, #34039381, … |
| maximal normal subgroup of | C2×#23748745, #34039380, #34039381, … |
| maximal quotient of | #34039375, C2×#23748745 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9488, 52);