Finite Group DatabasebetaFinite Group Databasebeta| order | 23824 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#20238494 |
| Fitting | C4×C1489 ⋊ C4 |
| derived, Sylow | C1489 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #20238494 |
| commutator, hypocenter | C1489 | C42 |
| Frattini | C2 | C2×#20238494 |
| Fitting | C4×C1489 | C4 |
| socle | C2×C1489 | C2×C4 |
| prime radical, cosocle | C2×D1489 | C22 |
| LCS | G ▷ C1489 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5956 |
1504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23824, 44);