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 | C2×C8×#3866 |
| Fitting | C2×C8×C37 ⋊ C4 |
| derived, Sylow | C37 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #3866 |
| commutator, hypocenter | C37 | C2×C4×C8 |
| Frattini | C4 | C22×#3866 |
| Fitting | C2×C8×C37 | C4 |
| socle | C22×C37 | C42 |
| prime radical | C22×D37 | C2×C4 |
| cosocle | C4×D37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#3866)⋊C16, #18009639, C4×C8×#3866, … |
| maximal normal subgroup of | (C2×#3866)⋊C16, #18009639, C4×C8×#3866, … |
| maximal quotient of | C2×C8×#64438, C8×D37⋊C8, C2×#64438⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1503);