Finite Group DatabasebetaFinite Group Databasebeta| order | 15248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C953 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16838374 |
| commutator, socle | C2×C953 | C2×C4 |
| Fitting, prime radical | C22×C953 | C4 |
| cosocle | Dic953 | C22 |
| hypercenter | C22 | #16838374 |
| hypocenter | C953 | M16 |
| LCS | G ▷ C2×C953 ▷ C953 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7624 |
Polycyclic presentation:
2^4,953|a^2=c,c^2=d,b^a=bd,e^a=e^511,e^c=e^952962 conjugacy classes — view the full character table.
| maximal subgroup of | #44479486, #44479487, C2×#29503965, … |
| maximal normal subgroup of | #44479486, #44479487, C2×#29503965, … |
| maximal quotient of | #44479481, C22⋊#21439330, #44479493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15248, 49);