Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D44 |
| Fitting | C24×C4×C11 ⋊ C2 |
| Sylow | C11 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D11 |
| commutator, cosocle | C2×C11 | C26 |
| Frattini | C2 | C25×D11 |
| Fitting | C24×C4×C11 | C2 |
| socle | C25×C11 | C22 |
| hypercenter | C24×C4 | D11 |
| hypocenter | C11 | C24×D4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13066856, #14675642, #14675988, … |
| maximal normal subgroup of | C2×#13066856, #14675642, #14675988, … |
| maximal quotient of | C24×(C2×D11)⋊C4, C24×C4⋊Dic11, C23×C4×D44, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19303);