Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C4×C457 ⋊ C2 |
| Sylow | C457 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=e,c^2=e,b^a=bd,f^b=f^456,f^c=f^4562300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416857, #44416859, #44416862, … |
| maximal normal subgroup of | #44416857, #44416859, #44416862, … |
| maximal quotient of | #44416624, C4⋊C4×Dic457, #44416648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 108);