Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#11763409 |
| Fitting | C2×C17×#121 ⋊ C2 |
| Sylow | C17 ⋊ C2×#540 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D17 |
| commutator, cosocle | C22×C17 | C25 |
| Frattini | C22 | C24×D17 |
| Fitting | C2×C17×#121 | C2 |
| socle | C23×C17 | C24 |
| hypercenter | C2×#121 | D17 |
| hypocenter | C17 | C2×#540 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
1260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17000371, #17000489, C4×#11763409, … |
| maximal normal subgroup of | #17000371, #17000489, C4×#11763409, … |
| maximal quotient of | C2×#14531388, C2×#14531425, C2×#14531426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17865);