Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×C83⋊C16 |
| derived, Sylow | C83 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D83 |
| commutator, hypocenter | C83 | C23×C16 |
| Frattini | C8 | C23×D83 |
| Fitting | C23×C8×C83 | C2 |
| socle, prime radical | C24×C83 | C8 |
| cosocle | C8×C83 | C24 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905540, C2×#24905541, #35319247, … |
| maximal normal subgroup of | C2×#24905540, C2×#24905541, #35319247, … |
| maximal quotient of | C22×C4×C83⋊C16, C22×C22⋊(C83⋊C16), C22×C4⋊(C83⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17603);