Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#11929434 |
| derived, Sylow | C157 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D157 |
| commutator, hypocenter | C157 | C82 |
| Frattini | C42 | C2×D157 |
| Fitting | C4×C8×C157 | C2 |
| socle, prime radical | C22×C157 | C42 |
| cosocle | C42×C157 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C4×C8 | |
74 conjugacy classes of subgroups.
2560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#11929434, #34098052, #34098055, … |
| maximal normal subgroup of | C16×#11929434, #34098052, #34098055, … |
| maximal quotient of | #34097963, C16×#11929434, C8×#14578929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 269);