Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C157 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #10597845 |
| commutator, hypocenter | C157 | C4×C16 |
| Frattini | C2×C4 | C2×#10597845 |
| Fitting | C2×C8×C157 | C4 |
| socle, prime radical | C22×C157 | C2×C8 |
| cosocle | C2×#11929434 | C22 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^129,g^b=g^156,g^c=g^156688 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 | C8×#14578957, #34115051, #34115175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1435);