Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #1276 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | D172 |
| commutator | C4×C43 | C4×C8 |
| Frattini | C2×C42 | C2×D43 |
| Fitting | C43×C43 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | C43 | D43 |
| hypocenter | C43 | #1276 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
208 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=d,b^2=e,c^2=f,d^2=g,b^a=bc,c^a=cf,e^a=ef,h^a=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24983348, #24983349, #24983420, … |
| maximal normal subgroup of | #24983348, #24983349, #24983420, … |
| maximal quotient of | #24983125, #24983129, #24983133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2343);