Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C293 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D293 |
| commutator | C22×C293 | C22×C4 |
| Fitting, prime radical | C25×C293 | C2 |
| socle, cosocle | C23×C293 | C23 |
| hypercenter | C25 | D293 |
| hypocenter | C293 | #379 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=f,b^a=bd,c^a=ce,g^a=g^2924700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156689, #49158699, #49158700, … |
| maximal normal subgroup of | #49156689, #49158699, #49158700, … |
| maximal quotient of | #49157008, #49157026, #49157056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 405);