Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C293 ⋊ C2 |
| Sylow | C293 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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=e,b^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^2922069 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49170292, #49170293, #49170299, … |
| maximal normal subgroup of | #49170292, #49170293, #49170299, … |
| maximal quotient of | #49161617, #49161619, #49161681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1212);