Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#10587528 |
| derived, Sylow | C17 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #3633 |
| commutator, hypocenter | C17 | C4×C32 |
| Frattini | C2×C4 | C2×#3633 |
| Fitting | C42×C17 | C8 |
| socle, prime radical | C22×C17 | C2×C16 |
| cosocle | C2×#63216 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C42 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10587528, #17981335, #17981341, … |
| maximal normal subgroup of | C8×#10587528, #17981335, #17981341, … |
| maximal quotient of | C8×#10587528, #17981341, #17981467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21592);