Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2388 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Frattini | C23 | C23×D11 |
| Fitting | C4×C11×C22⋊C4 | C2 |
| hypercenter | C4×C22⋊C4 | D11 |
| hypocenter | C11 | #2388 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
944 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^10,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648741, #14648746, #14725881, … |
| maximal normal subgroup of | #14648741, #14648746, #14725881, … |
| maximal quotient of | #14675453, #14675456, #14675486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7726);