Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting | C43×#392 ⋊ C2 |
| Sylow | C43 ⋊ #2825 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#392 | C2 |
| hypercenter | #392 | D43 |
| hypocenter | C43 | #2825 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #392 | |
522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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=eg,b^a=be,c^a=cf,h^a=h^42,c^b=cg,d^b=def,d^c=de,h^d=h^42488 conjugacy classes — view the full character table.
| maximal subgroup of | D43×#2825, C2×#19142684, #25302985, … |
| maximal normal subgroup of | D43×#2825, C2×#19142684, #25302985, … |
| maximal quotient of | #25027230, #25027396, #25027454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 12599);