Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C157 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D157 |
| commutator | C22×C157 | C22×C4 |
| Fitting, prime radical | C25×C157 | C2 |
| socle, cosocle | C23×C157 | C23 |
| hypercenter | C25 | D157 |
| hypocenter | C157 | #379 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=f,b^a=bd,c^a=ce,g^a=g^1562524 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34098040, #34100050, #34100051, … |
| maximal normal subgroup of | #34098040, #34100050, #34100051, … |
| maximal quotient of | #34098359, #34098377, #34098407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 405);