Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#10587467 |
| derived, Sylow | C17 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #595 |
| commutator, hypocenter | C17 | C4×C32 |
| Frattini | C2×C8 | C2×#595 |
| Fitting | C4×C8×C17 | C4 |
| socle, prime radical | C22×C17 | C2×C16 |
| cosocle | C2×#63214 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4×C8 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10587467, #17949087, #17949089, … |
| maximal normal subgroup of | C8×#10587467, #17949087, #17949089, … |
| maximal quotient of | C8×#10587467, #17949095, #17949391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19614);