Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C43 ⋊ C2 |
| Sylow | C43 ⋊ #1438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D43 |
| commutator | C23×C43 | C22×C4 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | #1438 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
1168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,43|a^2=g,b^a=bd,c^a=ce,c^b=cf,h^c=h^42884 conjugacy classes — view the full character table.
| maximal subgroup of | #24989166, D43×#1438, C2×#19132834, … |
| maximal normal subgroup of | #24989166, D43×#1438, C2×#19132834, … |
| maximal quotient of | #24984518, #24984519, #24984523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 2749);