Finite Group DatabasebetaFinite Group Databasebeta| order | 4448 |
| isoclinism | isoclinic class of D139 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D139 |
| unambiguous semidirect product | C139⋊C25 |
| unambiguous semidirect product | (C2×C139)⋊C24 |
| Fitting, socle | C24×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D139 |
| commutator, cosocle, hypocenter | C139 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2224 |
1136 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4448, 195);