Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×#3633 |
| unambiguous semidirect product | #595⋊(C22×C8) |
| Fitting | C22×C4×C17 ⋊ C8 |
| derived, Sylow | C17 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #3633 |
| commutator, hypocenter | C17 | C22×C4×C8 |
| Frattini | C2 | C23×#3633 |
| Fitting | C22×C4×C17 | C8 |
| socle | C23×C17 | C2×C8 |
| prime radical | C23×D17 | C2×C4 |
| cosocle | C2×#595 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C4 | |
760 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 407 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#3633)⋊C8, #17981562, C2×#14545791, … |
| maximal normal subgroup of | C2×(C2×#3633)⋊C8, #17981562, C2×#14545791, … |
| maximal quotient of | C22×C8×#3633, C22×#11763893, C2×M16×#3633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21745);