Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#342 ⋊ C2 |
| Sylow | C11 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #66935 |
| commutator, cosocle | C24×C11 | C23 |
| Frattini | C24 | C22×D11 |
| Fitting | C11×#342 | C2 |
| socle | C22×C11 | #120 |
| hypercenter | #342 | D11 |
| hypocenter | C11 | #2021 |
| LCS | G ▷ C24×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|b^a=bd,c^a=ce,f^a=fg,h^a=h^10,c^b=cf,h^b=h^10,d^c=dg,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14665803, #14665808, #14665821, … |
| maximal normal subgroup of | #14665803, #14665808, #14665821, … |
| maximal quotient of | #14653972, #14653979, #14653986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5637);