Finite Group DatabasebetaFinite Group Databasebeta| order | 15952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C997 ⋊ C2 |
| Sylow | C997 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D997 |
| commutator, socle, cosocle | C2×C997 | C23 |
| Frattini | C2 | C22×D997 |
| Fitting | C2×C4×C997 | C2 |
| hypercenter | C2×C4 | D997 |
| hypocenter | C997 | #41 |
| LCS | G ▷ C2×C997 ▷ C997 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7976 |
Polycyclic presentation:
2^4,997|c^2=d,b^a=bd,e^b=e^9963994 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44542227, #44542229, #44542307, … |
| maximal normal subgroup of | #44542227, #44542229, #44542307, … |
| maximal quotient of | #44542258, #44542260, C4×C22⋊D997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15952, 40);