Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#123 ⋊ C2 |
| Sylow | C11 ⋊ #2412 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C2×C11×#123 | C2 |
| prime radical | C2×#66990 | C2 |
| hypercenter | C2×#123 | D11 |
| hypocenter | C11 | #2412 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
814 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14791118, #14791121, #14806930, … |
| maximal normal subgroup of | #14791118, #14791121, #14806930, … |
| maximal quotient of | #14675654, #14675731, #14676596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7902);