Finite Group DatabasebetaFinite Group Databasebeta| order | 4496 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C281 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D281 |
| commutator, hypocenter | C281 | C16 |
| Fitting, cosocle | C8×C281 | C2 |
| socle, prime radical | C2×C281 | C8 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 297 |
| transitive degree | μt(G) = 4496 |
Polycyclic presentation:
2^4,281|a^2=b,b^2=c,c^2=d,e^a=e^2801136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4496, 15);