Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C293 ⋊ C2 |
| Sylow | C293 ⋊ C4×#41 |
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=f,c^2=f,d^2=e,b^a=be,g^c=g^2922960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49158589, #49158594, #49158804, … |
| maximal normal subgroup of | #49158589, #49158594, #49158804, … |
| maximal quotient of | #49161124, #117×Dic293, C4×#22627584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1017);