Finite Group DatabasebetaFinite Group Databasebeta| order | 19792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C1237 ⋊ C2 |
| Sylow | C1237 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1237 |
| commutator, socle, cosocle | C2×C1237 | C23 |
| Fitting | Q8×C1237 | C2 |
| hypercenter | Q8 | D1237 |
| hypocenter | C1237 | #41 |
| LCS | G ▷ C2×C1237 ▷ C1237 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9896 |
Polycyclic presentation:
2^4,1237|c^2=d,b^a=bd,e^a=e^1236,e^b=e^1236,e^c=e^12363100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19792, 41);