Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C42×C277 ⋊ C2 |
| Sylow | C277 ⋊ #532 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D277 |
| commutator, socle, cosocle | C22×C277 | C24 |
| Frattini | C22 | C23×D277 |
| Fitting | C2×C42×C277 | C2 |
| hypercenter | C2×C42 | D277 |
| hypocenter | C277 | #532 |
| LCS | G ▷ C22×C277 ▷ C277 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8864 |
Polycyclic presentation:
2^6,277|c^2=f,d^2=e,b^a=be,c^a=cf,g^a=g^2764444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #47981565, #47981567, #47981583, … |
| maximal normal subgroup of | #47981565, #47981567, #47981583, … |
| maximal quotient of | #47985574, #47985631, #47985657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 1099);