Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×Q8×D17 |
| Fitting | D4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | D4×Q8×C17 | C2 |
| prime radical | C2×D4×D17 | C22 |
| hypercenter | D4×Q8 | D17 |
| hypocenter | C17 | C2×D4×Q8 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1627, D17×#1637, D17×#1651, … |
| maximal normal subgroup of | D17×#1627, D17×#1637, D17×#1651, … |
| maximal quotient of | Q8×C22⋊C4×D17, D4×C4⋊C4×D17, Q8×C4⋊C4×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17980);