Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×#63241 |
| derived, Sylow | C17 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #3633 |
| commutator, hypocenter | C17 | C8×C16 |
| Frattini | C2×C4 | C2×#3633 |
| Fitting | C2×C8×C17 | C8 |
| socle, prime radical | C22×C17 | C4×C8 |
| cosocle | C4×#3624 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#63241, #17981090, #17981091, … |
| maximal normal subgroup of | C16×#63241, #17981090, #17981091, … |
| maximal quotient of | C16×#63241, #17981090, #17981196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21524);