Finite Group DatabasebetaFinite Group Databasebeta| order | 16976 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1061⋊C8 |
| derived, Sylow | C1061 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16862558 |
| commutator, hypocenter | C1061 | C2×C8 |
| Frattini | C2 | C2×#16862558 |
| Fitting | C4×C1061 | C4 |
| socle | C2×C1061 | C2×C4 |
| prime radical | C2×D1061 | C4 |
| cosocle | Dic1061 | C22 |
| LCS | G ▷ C1061 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8488 |
Polycyclic presentation:
2^4,1061|a^2=c,c^2=d,e^a=e^958,e^b=e^1060,e^c=e^10601076 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16862558, #46800684, #46800692, … |
| maximal normal subgroup of | C8×#16862558, #46800684, #46800692, … |
| maximal quotient of | C4×#22555123, #46800687, #46800697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16976, 48);