Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#3866 |
| Fitting | C42×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #3866 |
| commutator, hypocenter | C37 | C43 |
| Frattini | C22 | C22×#3866 |
| Fitting | C42×C37 | C4 |
| socle | C22×C37 | C22×C4 |
| prime radical, cosocle | C22×D37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C42 | |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #18009423, C4×C8×#3866, #97×#3866, … |
| maximal normal subgroup of | #18009423, C4×C8×#3866, #97×#3866, … |
| maximal quotient of | #95×#3866, C4×(C2×#3866)⋊C4, C4×C8×#3866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1483);