Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14578954 |
| Fitting | C23×C4×C157 ⋊ C2 |
| Sylow | C157 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D157 |
| commutator, cosocle | C2×C157 | C25 |
| Frattini | C2 | C24×D157 |
| Fitting | C23×C4×C157 | C2 |
| socle | C23×C157 | C23 |
| hypercenter | C23×C4 | D157 |
| hypocenter | C157 | C22×#41 |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
890 conjugacy classes of subgroups.
2536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34100047, #34100053, #34100062, … |
| maximal normal subgroup of | #34100047, #34100053, #34100062, … |
| maximal quotient of | C22×#19097728, C22×#19097730, C22×C4×C22⋊D157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1376);