Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×#41×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2404 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D131 |
| commutator, socle, cosocle | C23×C131 | C24 |
| Fitting | C22×#41×C131 | C2 |
| hypercenter | C22×#41 | D131 |
| hypocenter | C131 | #2404 |
| LCS | G ▷ C23×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
1056 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|b^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^1302638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 7825);