Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C271⋊C8 |
| derived, Sylow | C271 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D271 |
| commutator, hypocenter | C271 | C22×C8 |
| Frattini | C4 | C22×D271 |
| Fitting | C22×C4×C271 | C2 |
| socle | C23×C271 | C4 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31773651, #31773652, #31773659, … |
| maximal normal subgroup of | #31773651, #31773652, #31773659, … |
| maximal quotient of | C2×C4×C271⋊C8, C2×C22⋊(C271⋊C8), C2×C4⋊(C271⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 148);