Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D271 |
| Fitting | M16×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D271 |
| commutator, socle | C2×C271 | C22×C4 |
| Fitting | M16×C271 | C2 |
| hypercenter | M16 | D271 |
| hypocenter | C271 | C2×M16 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D271, #101×D271, #31773878, … |
| maximal normal subgroup of | #100×D271, #101×D271, #31773878, … |
| maximal quotient of | #97×D271, M16×Dic271, #31773849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 149);