Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C457 ⋊ C2 |
| Sylow | C457 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^4561607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D457, C2×#28410581, #44417573, … |
| maximal normal subgroup of | #137×D457, C2×#28410581, #44417573, … |
| maximal quotient of | #44416775, #44416784, #44416816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 175);