Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#72310668 |
| derived | #5464 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11715754 |
| commutator, hypocenter | #5464 | C22×C4 |
| Frattini | C23 | C22×#1020 |
| Fitting | C22×#3549 | D3 |
| socle | C24 | C2×#1020 |
| prime radical | C22×#3549⋊C3 | C2 |
| cosocle | C2×#5464 | C23 |
| LCS | G ▷ #5464 | |
| UCS | C1 ◁ C22 | |
11329 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 11329 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×#11715754, C2×#72341123 |
| maximal normal subgroup of | C2×C4×#11715754, C2×#72341123 |
Past the SmallGroups library coverage — no SmallGroups id.