Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D37⋊C8 |
| derived, Sylow | C37 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #3866 |
| commutator, hypocenter | C37 | C2×C4×C8 |
| Frattini | C22 | C22×#3866 |
| Fitting | C42×C37 | C4 |
| socle | C22×C37 | C22×C4 |
| prime radical | C22×D37 | C2×C4 |
| cosocle | C2×Dic37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #18009425, #18009427, #18009430, … |
| maximal normal subgroup of | #18009425, #18009427, #18009430, … |
| maximal quotient of | C8×D37⋊C8, #18009790, #18009794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1505);