Finite Group DatabasebetaFinite Group Databasebeta| order | 15208 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1901 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #21439211 |
| commutator, hypocenter | C1901 | C8 |
| Fitting, socle, prime radical | C2×C1901 | C4 |
| cosocle | Dic1901 | C2 |
| LCS | G ▷ C1901 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15208 |
Polycyclic presentation:
2^3,1901|a^2=b,b^2=c,d^a=d^1683,d^b=d^1900958 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#29503535, D1901⋊C8, #44477403, … |
| maximal normal subgroup of | C2×#29503535, D1901⋊C8, #44477403, … |
| maximal quotient of | #44477397, C2×#29503535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15208, 13);