Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C8×C43 ⋊ C2 |
| Sylow | C43 ⋊ #2965 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D43 |
| commutator, socle | C22×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C2×C4×C8×C43 | C2 |
| hypercenter | C2×C4×C8 | D43 |
| hypocenter | C43 | #2965 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C2×C4×C8 | |
412 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,h^a=h^421400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24987333, #24987335, #24987340, … |
| maximal normal subgroup of | #24987333, #24987335, #24987340, … |
| maximal quotient of | #25094809, #25094816, C4×#14582970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13476);