Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #123×C277 ⋊ C2 |
| Sylow | C277 ⋊ #534 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Fitting | #123×C277 | C2 |
| hypercenter | #123 | D277 |
| hypocenter | C277 | #534 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C22 ◁ #123 | |
346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4432 |
Polycyclic presentation:
2^6,277|b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^276,g^c=g^2761954 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47984812 |
| maximal normal subgroup of | #47984812 |
| maximal quotient of | #47985741, #47985744, #47985778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1110);