Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C457 ⋊ SD32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^456,c^b=cd,d^b=de1607 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D457, C2×#28410496, #44417206, … |
| maximal normal subgroup of | SD32×D457, C2×#28410496, #44417206, … |
| maximal quotient of | #44416578, #44416580, #44416604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 90);