Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623099 |
| Fitting | C2×C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#556 |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645400, #14720025, #14720031, … |
| maximal normal subgroup of | #14645400, #14720025, #14720031, … |
| maximal quotient of | C2×#13071510, C2×#13071561, C2×#13071574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18058);