Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#88128 |
| Fitting | C22×C42×C13 ⋊ C2 |
| Sylow | C13 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C22×C42×C13 | C2 |
| socle | C24×C13 | C23 |
| hypercenter | C22×C42 | D13 |
| hypocenter | C13 | C22×#127 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754402, #15769456, #15769483, … |
| maximal normal subgroup of | #15754402, #15769456, #15769483, … |
| maximal quotient of | C22×#11718596, C22×#11718600, C2×C4×#88128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17782);