Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2789 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, prime radical, cosocle | C23×C11 | C24 |
| Fitting | C11×#387 | C2 |
| hypercenter | #387 | D11 |
| hypocenter | C11 | #2789 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #387 | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=efg,b^2=ef,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14961720, #14961723, #14961725, … |
| maximal normal subgroup of | #14961720, #14961723, #14961725, … |
| maximal quotient of | #14681676, #14681680, #14682085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12265);