Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#14578929 |
| derived, Sylow | C157 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D157 |
| commutator, hypocenter | C157 | C4×C16 |
| Frattini | C2×C8 | C2×D157 |
| Fitting | C4×C8×C157 | C2 |
| socle, prime radical | C22×C157 | C2×C8 |
| cosocle | C2×C8×C157 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
2560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11929434, C8×#14578929, #34098052, … |
| maximal normal subgroup of | C16×#11929434, C8×#14578929, #34098052, … |
| maximal quotient of | C8×#14578929, #34098054, #34098214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 323);