Finite Group DatabasebetaFinite Group Databasebeta| order | 4496 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#11765499 |
| Fitting | C4×C281 ⋊ C4 |
| Sylow | C281 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#11765499 |
| commutator, socle | C2×C281 | C2×C4 |
| Fitting | C4×C281 | C4 |
| prime radical, cosocle | C2×D281 | C22 |
| hypercenter | C4 | #11765499 |
| hypocenter | C281 | C4⋊C4 |
| LCS | G ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1124 |
Polycyclic presentation:
2^4,281|a^2=d,b^2=c,b^a=bc,e^a=e^228,e^d=e^280290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4496, 46);