Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C293 ⋊ C4 |
| Sylow | C293 ⋊ #427 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=e,b^2=d,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^138,g^e=g^2921196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173847, #49173848, #49173852, … |
| maximal normal subgroup of | #49173847, #49173848, #49173852, … |
| maximal quotient of | #49174332, #49174333, #49174334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1559);