Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×D457 |
| Fitting | C2×D4×C457 ⋊ C2 |
| Sylow | C457 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D457 |
| commutator, cosocle | C2×C457 | C24 |
| Frattini | C2 | C23×D457 |
| Fitting | C2×D4×C457 | C2 |
| socle | C22×C457 | C23 |
| hypercenter | C2×D4 | D457 |
| hypocenter | C457 | C22×D4 |
| LCS | G ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3656 |
2300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D457, #100×D457, #102×D457, … |
| maximal normal subgroup of | #99×D457, #100×D457, #102×D457, … |
| maximal quotient of | C2×C22⋊C4×D457, C2×C4⋊C4×D457, C4×D4×D457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 182);