Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×#11763740 |
| derived, Sylow | C17 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #595 |
| commutator, hypocenter | C17 | C22×C32 |
| Frattini | C8 | C22×#595 |
| Fitting | C2×C16×C17 | C4 |
| socle | C22×C17 | C2×C16 |
| prime radical | C22×D17 | C16 |
| cosocle | #63214 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #17949390, #17949409, #17949410, … |
| maximal normal subgroup of | #17949390, #17949409, #17949410, … |
| maximal quotient of | C4×#11763740, C2×#14543889, #17962567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20929);