Finite Group DatabasebetaFinite Group Databasebeta| order | 5392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#14582106 |
| derived, Sylow | C337 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D337 |
| commutator, hypocenter | C337 | C2×C8 |
| Frattini | C4 | C2×D337 |
| Fitting | C2×C4×C337 | C2 |
| socle | C22×C337 | C4 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
1360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5392, 22);