Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16864653 |
| Fitting | C2×D4×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D271 |
| commutator | C2×C271 | C24 |
| Frattini | C2 | C23×D271 |
| Fitting | C2×D4×C271 | C2 |
| socle | C22×C271 | C23 |
| hypercenter | C2×D4 | D271 |
| hypocenter | C271 | C2×#41 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31773869, #31773878, #31773890, … |
| maximal normal subgroup of | #31773869, #31773878, #31773890, … |
| maximal quotient of | C2×#22576116, C2×#22576118, C2×(C22⋊D271)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 188);