Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C22×#72209705 |
| Fitting | C22×#17309 ⋊ D3 |
| derived | #11709340 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | #11714280 |
| commutator, cosocle, hypocenter | #11709340 | C23 |
| Frattini | C24 | C22×#1020 |
| Fitting | C22×#17309 | D3 |
| socle | C25 | #5934 |
| hypercenter | C24 | #85558 |
| LCS | G ▷ #11709340 | |
| UCS | C1 ◁ C23 ◁ C24 | |
22579 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 22579 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72266550 |
Past the SmallGroups library coverage — no SmallGroups id.