Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C4 |
| direct product | C22×#11714184 |
| Fitting | C22×#3027 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C25 |
| Frattini | C23 | C24×S4 |
| Fitting | C22×#3027 | D3 |
| hypercenter | C22×C4 | #1020⋊C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
32678 conjugacy classes of subgroups; only the 535 normal subgroups are shown.
This group has 32678 conjugacy classes of subgroups — too many to draw. Only its 535 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72236955, C2×#72240988, #72343876, … |
| maximal normal subgroup of | C2×#72236955, C2×#72240988, #72343876, … |
| maximal quotient of | C2×#72246879 |
Past the SmallGroups library coverage — no SmallGroups id.