Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1776 |
272 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,b^a=bd,c^a=cg,h^a=h^82,d^b=dg,e^b=eg,h^b=h^82,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319694, #35319700, #35319825, … |
| maximal normal subgroup of | #35319694, #35319700, #35319825, … |
| maximal quotient of | #35295604, #35295609, #35295626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4410);