Finite Group DatabasebetaFinite Group Databasebeta| order | 29248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C457 ⋊ C2 |
| Sylow | C457 ⋊ #538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D457 |
| commutator, socle, cosocle | C22×C457 | C24 |
| Fitting | C22⋊Q8×C457 | C2 |
| hypercenter | C22⋊Q8 | D457 |
| hypocenter | C457 | #538 |
| LCS | G ▷ C22×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^6,457|b^2=f,b^a=be,c^a=cf,d^a=de,g^a=g^456,c^b=ce,g^b=g^456,g^c=g^4563214 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29248, 1139);