Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11929441 |
| derived, Sylow | C157 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10597845 |
| commutator, hypocenter | C157 | C82 |
| Frattini | C2×C4 | C2×#10597845 |
| Fitting | C2×C8×C157 | C4 |
| socle, prime radical | C22×C157 | C42 |
| cosocle | C4×Dic157 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
688 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11929441, #34115047, #11929441⋊C16, … |
| maximal normal subgroup of | C16×#11929441, #34115047, #11929441⋊C16, … |
| maximal quotient of | #34114958, C16×#11929441, C8×#14578957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1389);