Finite Group DatabasebetaFinite Group Databasebeta| order | 4496 |
| automorphism | Aut(G) order 2517760 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2248 |
| Fitting | C8×C281 ⋊ C2 |
| Sylow | C281 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1124 |
| commutator, cosocle | C4×C281 | C22 |
| Frattini | C4 | C2×D281 |
| Fitting | C8×C281 | C2 |
| socle | C2×C281 | D4 |
| hypercenter | C8 | D281 |
| hypocenter | C281 | D8 |
| LCS | G ▷ C4×C281 ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2248 |
Polycyclic presentation:
2^4,281|c^2=d,b^a=bc,c^a=cd,e^a=e^280,c^b=cd,e^b=e^2801127 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6744, D11240, D15736, … |
| maximal quotient of | D6744, D11240, D15736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4496, 26);