Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C457 ⋊ C2 |
| Sylow | C457 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D457 |
| commutator, socle | C2×C457 | C22×C4 |
| Fitting | M16×C457 | C2 |
| prime radical | #20300741 | C2 |
| cosocle | C4×C457 | C23 |
| hypercenter | M16 | D457 |
| hypocenter | C457 | #131 |
| LCS | G ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|a^2=d,d^2=e,f^a=f^456,c^b=ce,f^c=f^4562300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44416891, #44416893, #44416896, … |
| maximal normal subgroup of | #44416891, #44416893, #44416896, … |
| maximal quotient of | #44416734, #44416735, #44416742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 154);