Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C83⋊C8 |
| derived, Sylow | C83 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D83 |
| commutator, hypocenter | C83 | C42×C8 |
| Frattini | C22×C4 | C22×D83 |
| Fitting | C43×C83 | C2 |
| socle, prime radical | C23×C83 | C22×C4 |
| cosocle | C22×C4×C83 | C23 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C43 | |
408 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35290931, C4×C8×C83⋊C8, C4×#19127422, … |
| maximal normal subgroup of | #35290931, C4×C8×C83⋊C8, C4×#19127422, … |
| maximal quotient of | C4×C8×C83⋊C8, C4×#19127422, #97×C83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4192);