Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#13063257 |
| Sylow | C43 ⋊ C22×#106 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D172 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C23×C8×C43 | C2 |
| socle | C24×C43 | D4 |
| hypercenter | C23×C8 | D43 |
| hypocenter | C43 | C22×#106 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
600 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #25002491, #25002493, #25002501, … |
| maximal normal subgroup of | #25002491, #25002493, #25002501, … |
| maximal quotient of | C22×#14582650, C2×#19133351, C2×#19133366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 13082);