Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #383×C73 ⋊ C4 |
| Sylow | C73 ⋊ #14678 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#64408 |
| commutator, socle | C23×C73 | C23×C4 |
| Fitting | #383×C73 | C4 |
| prime radical, cosocle | C23×D73 | C24 |
| hypercenter | #383 | #64408 |
| hypocenter | C73 | #14678 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #383 | |
1182 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=h,c^2=g,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^b=def,i^b=i^27,d^c=de,i^h=i^72556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1099173);