Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C43 · Schur multiplier (H2) = C2×C4 |
| direct product | C43×#1687 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C43 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C42×C43 ◁ G | |
198 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 68 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×#12324, C43×#12325, C43×#12348, … |
| maximal normal subgroup of | C43×#12324, C43×#12325, C43×#12348, … |
| maximal quotient of | C43×#8652, C43×#9229, C43×#9571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 419);