Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C43 · Schur multiplier (H2) = C23 |
| direct product | C43×#2133 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | C2×#99 |
| commutator | C2×C4 | C22×C4×C43 |
| Frattini, cosocle | C2×Q8 | C23×C43 |
| prime radical | C2×#41×C43 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C23×C43 ◁ C22×Q8×C43 ◁ G | |
230 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
989 conjugacy classes — view the full character table.
| maximal subgroup of | C43×#12709, C43×#12710, C43×#12729, … |
| maximal normal subgroup of | C43×#12709, C43×#12710, C43×#12729, … |
| maximal quotient of | C43×#11432, C43×#11448, C43×#11480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 865);