Finite Group DatabasebetaFinite Group Databasebeta| order | 20752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C1297 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19104447 |
| commutator, hypocenter | C1297 | C2×C8 |
| Frattini | C2 | C2×#19104447 |
| Fitting | C4×C1297 | C4 |
| socle | C2×C1297 | C2×C4 |
| prime radical | C2×D1297 | C4 |
| cosocle | Dic1297 | C22 |
| LCS | G ▷ C1297 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10376 |
Polycyclic presentation:
2^4,1297|a^2=c,c^2=d,e^a=e^1261,e^b=e^1296,e^c=e^12961312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20752, 48);