Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#14578957 |
| derived, Sylow | C157 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #10597845 |
| commutator, hypocenter | C157 | C22×C16 |
| Frattini | C4 | C22×#10597845 |
| Fitting | C22×C4×C157 | C4 |
| socle, prime radical | C23×C157 | C8 |
| cosocle | #11929434 | C23 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
688 conjugacy classes — view the full character table.
| maximal subgroup of | #34115174, #34115175, #34115190, … |
| maximal normal subgroup of | #34115174, #34115175, #34115190, … |
| maximal quotient of | C2×C4×#14578957, C2×C22⋊#14578957, C2×C4⋊#14578957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1602);