Finite Group DatabasebetaFinite Group Databasebeta| order | 9488 |
| automorphism | Aut(G) order 11233792 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4744 |
| Fitting | C8×C593 ⋊ C2 |
| Sylow | C593 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D2372 |
| commutator, cosocle | C4×C593 | C22 |
| Frattini | C4 | C2×D593 |
| Fitting | C8×C593 | C2 |
| socle | C2×C593 | D4 |
| hypercenter | C8 | D593 |
| hypocenter | C593 | D8 |
| LCS | G ▷ C4×C593 ▷ C2×C593 ▷ C593 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,593|c^2=d,b^a=bc,c^a=cd,e^a=e^592,c^b=cd,e^b=e^5922375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34039226, D9488, #34039228, … |
| maximal normal subgroup of | #34039226, D9488, #34039228, … |
| maximal quotient of | #34039207, #34039219, D9488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9488, 26);