Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#21440611 |
| Fitting | C25×C241 ⋊ C2 |
| Sylow | C241 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D241 |
| commutator, cosocle | C22×C241 | C24 |
| Frattini | C22 | C23×D241 |
| Fitting | C25×C241 | C2 |
| socle | C23×C241 | C23 |
| hypercenter | C25 | D241 |
| hypocenter | C241 | C2×#120 |
| LCS | G ▷ C22×C241 ▷ C241 | |
| UCS | C1 ◁ C23 ◁ C25 | |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3856 |
3868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44507850, #44507896, #44507898, … |
| maximal normal subgroup of | #44507850, #44507896, #44507898, … |
| maximal quotient of | C2×#29507573, C2×#29507590, C2×#29507596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1035);