Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1292 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C43⋊#95 |
| commutator | C2×C4×C43 | C42 |
| Frattini | C2×C42 | C2×D43 |
| Fitting | C43×#423 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | #423 | D43 |
| hypocenter | C43 | #1292 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
152 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^42620 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#1292, C2×#19132469, #24986542, … |
| maximal normal subgroup of | D43×#1292, C2×#19132469, #24986542, … |
| maximal quotient of | #24983134, #24983139, #24983141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2384);