Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C24×C4×C11 ⋊ C2 |
| Sylow | C11 ⋊ #2847 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C24×C4×C11 | C2 |
| hypercenter | C24×C4 | D11 |
| hypocenter | C11 | #2847 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C24×C4 | |
1224 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 237 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|b^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^10364 conjugacy classes — view the full character table.
| maximal subgroup of | #14649336, #14649338, #14649356, … |
| maximal normal subgroup of | #14649336, #14649338, #14649356, … |
| maximal quotient of | #14684933, #14684988, #14685006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12792);