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×C4×#64438 |
| derived, Sylow | C37 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #3866 |
| commutator, hypocenter | C37 | C2×C4×C8 |
| Frattini | C22 | C22×#3866 |
| Fitting | C22×C4×C37 | C4 |
| socle, prime radical | C23×C37 | C2×C4 |
| cosocle | C2×Dic37 | C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C4 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #18009418, #18009429, #18009432, … |
| maximal normal subgroup of | #18009418, #18009429, #18009432, … |
| maximal quotient of | C2×C8×#64438, C2×#14558374, M16×#64438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1504);