Finite Group DatabasebetaFinite Group Databasebeta| order | 15952 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D997 |
| unambiguous semidirect product | C997⋊C24 |
| unambiguous semidirect product | (C2×C997)⋊C23 |
| Fitting, socle | C23×C997 ⋊ C2 |
| derived, Sylow | C997 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D997 |
| commutator, cosocle, hypocenter | C997 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C997 | C2 |
| LCS | G ▷ C997 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7976 |
4000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D997, C2×#30630105, #44542269, … |
| maximal normal subgroup of | C22⋊C4×D997, C2×#30630105, #44542269, … |
| maximal quotient of | C22×C4×D997, C23×Dic997, C2×D4×D997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15952, 42);