Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#64438 |
| derived, Sylow | C37 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #3866 |
| commutator, hypocenter | C37 | C23×C8 |
| Frattini | C2 | C23×#3866 |
| Fitting, socle, prime radical | C24×C37 | C4 |
| cosocle | Dic37 | C24 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C24 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2368 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558399, #18010262, C22⋊C4×#64438, … |
| maximal normal subgroup of | C2×#14558399, #18010262, C22⋊C4×#64438, … |
| maximal quotient of | C22×C4×#64438, C22×C22⋊#64438, C22×C4⋊#64438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1619);