Finite Group DatabasebetaFinite Group Databasebeta| order | 4448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C139 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D139 |
| commutator, socle | C2×C139 | C22×C4 |
| Fitting, prime radical | #41×C139 | C2 |
| cosocle | C4×C139 | C23 |
| hypercenter | #41 | D139 |
| hypocenter | C139 | #131 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2224 |
Polycyclic presentation:
2^5,139|a^2=d,d^2=e,f^a=f^138,c^b=ce710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4448, 153);