Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C157 ⋊ #405 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^1562536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34098221, #34098223, #34098224, … |
| maximal normal subgroup of | #34098221, #34098223, #34098224, … |
| maximal quotient of | C8×#14578938, #34098419, #34098425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 504);