Finite Group DatabasebetaFinite Group Databasebeta| order | 17496 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#72221857 |
| Fitting | C2×#14550423 ⋊ C22 |
| derived, Sylow | #14550423 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72221857 |
| commutator, cosocle, hypocenter | #14550423 | C23 |
| Frattini | C32×C9 | C2×D3×C3⋊D3 |
| Fitting | C2×#14550423 | C22 |
| socle | C2×C3 | #72221854 |
| LCS | G ▷ #14550423 | |
| UCS | C1 ◁ C2 | |
1915 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 1915 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221873 |
| maximal normal subgroup of | C2×#72221873 |
Past the SmallGroups library coverage — no SmallGroups id.