Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #391×C139 ⋊ C2 |
| Sylow | C139 ⋊ #2855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D139 |
| commutator, socle, cosocle | C23×C139 | C24 |
| Fitting | #391×C139 | C2 |
| prime radical | C23×D139 | C23 |
| hypercenter | #391 | D139 |
| hypocenter | C139 | #2855 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ #391 | |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8896 |
Polycyclic presentation:
2^7,139|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^138,h^b=h^138,h^c=h^1381976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 12851);