Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C26×C11 ⋊ C2 |
| Sylow | C11 ⋊ #2846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C26×C11 | C2 |
| hypercenter | C26 | D11 |
| hypocenter | C11 | #2846 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C26 | |
3422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|b^a=be,c^a=cf,d^a=dg,h^a=h^10364 conjugacy classes — view the full character table.
| maximal subgroup of | #14785350, #14785352, #14786217, … |
| maximal normal subgroup of | #14785350, #14785352, #14786217, … |
| maximal quotient of | #14684929, #14684982, #14684988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12787);