Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | #95×Dic17 |
| Sylow | C17 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D17 |
| commutator | C2×C17 | C43 |
| Fitting | C2×C17×#95 | C2 |
| socle, prime radical, cosocle | C24×C17 | C23 |
| hypercenter | C2×#95 | D17 |
| hypocenter | C17 | C4×#95 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
752 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16925197, #327×Dic17, #16925202, … |
| maximal normal subgroup of | #16925197, #327×Dic17, #16925202, … |
| maximal quotient of | #16922243, #336×Dic17, #16939472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2729);