Finite Group DatabasebetaFinite Group Databasebeta| order | 23488 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic734 |
| Sylow | C367 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D367 |
| commutator, socle, prime radical, cosocle | C22×C367 | C24 |
| Fitting | C4×Q8×C367 | C2 |
| hypercenter | C4×Q8 | D367 |
| hypocenter | C367 | Q82 |
| LCS | G ▷ C22×C367 ▷ C367 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23488 |
3685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23488, 1280);