Finite Group DatabasebetaFinite Group Databasebeta| order | 27712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D4×C433 ⋊ C2 |
| Sylow | C433 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D433 |
| commutator, socle, cosocle | C23×C433 | C23 |
| Fitting | C22×D4×C433 | C2 |
| hypercenter | C22×D4 | D433 |
| hypocenter | C433 | #392 |
| LCS | G ▷ C23×C433 ▷ C433 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
322 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13856 |
Polycyclic presentation:
2^6,433|b^a=bd,c^a=ce,c^b=cf,g^c=g^4324342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27712, 457);