Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#19097821 |
| derived, Sylow | C157 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10597845 |
| commutator, hypocenter | C157 | C2×C32 |
| Frattini | C8 | C2×#10597845 |
| Fitting | C2×C8×C157 | C4 |
| socle, prime radical | C22×C157 | C16 |
| cosocle | #14578929 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C8 | |
34 conjugacy classes of subgroups.
688 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19097821, #34115241, #34115243, … |
| maximal normal subgroup of | C4×#19097821, #34115241, #34115243, … |
| maximal quotient of | C4×#19097821, C22⋊#19097821, C4⋊#19097821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1479);