Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D271 |
| Fitting | C2×C8×C271 ⋊ C2 |
| derived, Sylow | C271 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D271 |
| commutator, hypocenter | C271 | C22×C8 |
| Frattini | C4 | C22×D271 |
| Fitting | C2×C8×C271 | C2 |
| socle | C22×C271 | C2×C4 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D271)⋊C16, C4×C8×D271, #97×D271, … |
| maximal normal subgroup of | (C2×D271)⋊C16, C4×C8×D271, #97×D271, … |
| maximal quotient of | C4×C8×D271, C2×C8×Dic271, C22⋊C8×D271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 147);