Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | #95×D37 |
| Fitting | #95×C37 ⋊ C2 |
| Sylow | C37 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D37 |
| commutator | C2×C37 | C2×C42 |
| Fitting | #95×C37 | C2 |
| socle, cosocle | C23×C37 | C23 |
| prime radical | C23×D37 | C22 |
| hypercenter | #95 | D37 |
| hypocenter | C37 | C2×#95 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #95 | |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #327×D37, #328×D37, #17993097, … |
| maximal normal subgroup of | #327×D37, #328×D37, #17993097, … |
| maximal quotient of | #95×Dic37, #17992817, #17992824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 392);