Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#534 ⋊ C2 |
| Sylow | C11 ⋊ #3026 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#66990 |
| commutator, cosocle | C23×C11 | C24 |
| Frattini | C23 | C23×D11 |
| Fitting | C11×#534 | C2 |
| socle | C2×C11 | C2×#120 |
| hypercenter | #534 | D11 |
| hypocenter | C11 | #3026 |
| LCS | G ▷ C23×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #534 | |
800 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 145 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=be,c^a=cf,d^a=dg,f^b=fg,e^c=eg,h^c=h^10139 conjugacy classes — view the full character table.
| maximal subgroup of | #14785321, #14785322, #14785323, … |
| maximal normal subgroup of | #14785321, #14785322, #14785323, … |
| maximal quotient of | #14727605, #14727606, #14727612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13906);