Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D4×#4207⋊C2 |
| Fitting | D4×#737 ⋊ C22 |
| Sylow | #737 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#4207⋊C2 |
| commutator, cosocle | C2×#737 | C24 |
| Frattini, socle | C2×C3 | C22×#1113 |
| Fitting | D4×#737 | C22 |
| hypercenter | D4 | #4207⋊C2 |
| hypocenter | #737 | C22×D4 |
| LCS | G ▷ C2×#737 ▷ #737 | |
| UCS | C1 ◁ C2 ◁ D4 | |
1503 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D4×(#4207⋊C2)⋊C3 |
| maximal normal subgroup of | D4×(#4207⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.