Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C4×D271 |
| Fitting | C22⋊C4×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D271 |
| commutator | C2×C271 | C22×C4 |
| Fitting | C22⋊C4×C271 | C2 |
| socle | C22×C271 | C23 |
| hypercenter | C22⋊C4 | D271 |
| hypocenter | C271 | C2×C22⋊C4 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
132 conjugacy classes of subgroups.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D271, C2×C22⋊C4×D271, #117×D271, … |
| maximal normal subgroup of | #99×D271, C2×C22⋊C4×D271, #117×D271, … |
| maximal quotient of | #95×D271, #31773744, C22⋊C4×Dic271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 96);