Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C139 ⋊ #2835 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D139 |
| commutator, socle, cosocle | C23×C139 | C24 |
| Fitting | #393×C139 | C2 |
| prime radical | C24×C139 | C23 |
| hypercenter | #393 | D139 |
| hypocenter | C139 | #2835 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ #393 | |
380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8896 |
Polycyclic presentation:
2^7,139|a^2=g,b^2=e,c^2=ef,b^a=be,c^a=cf,h^a=h^138,c^b=cg,d^b=def,h^b=h^138,d^c=de,h^c=h^1381544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 12701);