Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #401×#6157 |
| Fitting | C53×#401 ⋊ C4 |
| Sylow | C53 ⋊ C4×#401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#6157 |
| commutator, socle | C23×C53 | C23×C4 |
| Fitting | C53×#401 | C4 |
| prime radical, cosocle | C23×D53 | C24 |
| hypercenter | #401 | #6157 |
| hypocenter | C53 | C4×#401 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #401 | |
1222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098361);