Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting, prime radical | C2×C11×#120 | C2 |
| hypercenter | C2×#120 | D11 |
| hypocenter | C11 | #2534 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=eg,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 | #14672064, #14672077, #14807160, … |
| maximal normal subgroup of | #14672064, #14672077, #14807160, … |
| maximal quotient of | #14675995, #14676491, #14676546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9397);