Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#14579268 |
| derived, Sylow | C317 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11929639 |
| commutator, hypocenter | C317 | C22×C8 |
| Frattini | C2 | C22×#11929639 |
| Fitting, socle, prime radical | C23×C317 | C4 |
| cosocle | Dic317 | C23 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C23 | |
76 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 228);