Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#3633 |
| Fitting | M16×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#3633 |
| commutator, socle | C2×C17 | C2×C4×C8 |
| Fitting | M16×C17 | C8 |
| prime radical | C22×D17 | C42 |
| cosocle | C4×#595 | C23 |
| hypercenter | M16 | #3633 |
| hypocenter | C17 | C8×M16 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ M16 | |
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 136 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #100×#3633, #101×#3633, #104×#3633, … |
| maximal normal subgroup of | #100×#3633, #101×#3633, #104×#3633, … |
| maximal quotient of | #97×#3633, #17981562, #17981590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21618);