Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C157 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #10597845 |
| commutator, hypocenter | C157 | C64 |
| Fitting | C16×C157 | C4 |
| socle, prime radical | C2×C157 | C32 |
| cosocle | #19097677 | C2 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^129,g^b=g^156688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23758112, D157⋊C64, #34115305, … |
| maximal normal subgroup of | C2×#23758112, D157⋊C64, #34115305, … |
| maximal quotient of | #34114951, C2×#23758112 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1388);