Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×#10596927 |
| derived, Sylow | C37 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #3866 |
| commutator, hypocenter | C37 | C4×C16 |
| Frattini | C2×C4 | C2×#3866 |
| Fitting | C42×C37 | C4 |
| socle, prime radical | C22×C37 | C2×C8 |
| cosocle | C2×#64436 | C22 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C42 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10596927, #18009508, #18009509, … |
| maximal normal subgroup of | C8×#10596927, #18009508, #18009509, … |
| maximal quotient of | C8×#10596927, #18009509, #18009634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1434);