Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic307 |
| unambiguous semidirect product | (C2×C307)⋊C42 |
| derived, Sylow | C307 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D307 |
| commutator, hypocenter | C307 | C2×C42 |
| Frattini | C22 | C22×D307 |
| Fitting | C22×C4×C307 | C2 |
| socle, prime radical | C23×C307 | C22 |
| cosocle | C22×C307 | C23 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
2480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34087641, #34087646, #34087648, … |
| maximal normal subgroup of | #34087641, #34087646, #34087648, … |
| maximal quotient of | C42×Dic307, C2×C307⋊#95, #34087733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 95);