Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C82×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1455 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D83 |
| commutator, socle | C22×C83 | C2×C42 |
| Fitting | C82×C83 | C2 |
| prime radical | C22×D83 | C42 |
| cosocle | C42×C83 | C23 |
| hypercenter | C82 | D83 |
| hypocenter | C83 | #1455 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C42 ◁ C82 | |
214 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cf,c^b=cg,h^c=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35314481, #1455×D83, C2×#24905765, … |
| maximal normal subgroup of | #35314481, #1455×D83, C2×#24905765, … |
| maximal quotient of | #35293779, #35293796, #35294840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2812);