Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×C79⋊C16 |
| derived, Sylow | C79 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D79 |
| commutator, hypocenter | C79 | C23×C16 |
| Frattini | C8 | C23×D79 |
| Fitting | C23×C8×C79 | C2 |
| socle, prime radical | C24×C79 | C8 |
| cosocle | C8×C79 | C24 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
2624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#23761477, C2×#23761478, #34203112, … |
| maximal normal subgroup of | C2×#23761477, C2×#23761478, #34203112, … |
| maximal quotient of | C22×C4×C79⋊C16, C22×C22⋊(C79⋊C16), C22×C4⋊(C79⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17603);