Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#14523266 |
| Fitting | C4×C509 ⋊ C4 |
| derived, Sylow | C509 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14523266 |
| commutator, hypocenter | C509 | C42 |
| Frattini | C2 | C2×#14523266 |
| Fitting | C4×C509 | C4 |
| socle | C2×C509 | C2×C4 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
524 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14523266, #30654269, #30654279, … |
| maximal normal subgroup of | C8×#14523266, #30654269, #30654279, … |
| maximal quotient of | (C2×#14523266)⋊C4, C8×#14523266, C4×#16861332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 44);