Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D17×#525 |
| Fitting | C17×#525 ⋊ C2 |
| Sylow | C17 ⋊ C2×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Frattini | C22 | C24×D17 |
| Fitting | C17×#525 | C2 |
| hypercenter | #525 | D17 |
| hypocenter | C17 | C2×#525 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×#1501, D17×#1504, #17001484, … |
| maximal normal subgroup of | D17×#1501, D17×#1504, #17001484, … |
| maximal quotient of | D17×#2280, D17×#2290, D17×#2296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17746);