Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#63254 |
| Fitting | D4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | D4×Q8×C17 | C2 |
| prime radical | C2×#63254 | C22 |
| hypercenter | D4×Q8 | D17 |
| hypocenter | C17 | Q8×#41 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #17010301, #17010309, #17010316, … |
| maximal normal subgroup of | #17010301, #17010309, #17010316, … |
| maximal quotient of | C4⋊C4×#63254, Q8×#10587563, Q8×#10587578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18087);