Finite Group DatabasebetaFinite Group Databasebeta| order | 15952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D997 |
| Fitting | C8×C997 ⋊ C2 |
| derived, Sylow | C997 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D997 |
| commutator, hypocenter | C997 | C2×C8 |
| Frattini | C4 | C2×D997 |
| Fitting | C8×C997 | C2 |
| socle | C2×C997 | C2×C4 |
| prime radical | C2×D997 | C4 |
| cosocle | C4×C997 | C22 |
| LCS | G ▷ C997 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7976 |
4000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D997, #44542240, C2×C8×D997, … |
| maximal normal subgroup of | C16×D997, #44542240, C2×C8×D997, … |
| maximal quotient of | C8×Dic997, #44542213, #44542230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15952, 21);