Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ #554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C4×Q8×C13 | C2 |
| prime radical | C2×D52 | C22 |
| hypercenter | C4×Q8 | D13 |
| hypocenter | C13 | #554 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|b^2=f,c^2=e,d^2=ef,b^a=bf,g^a=g^12,d^c=de145 conjugacy classes — view the full character table.
| maximal subgroup of | #13113907, #13113911, #13113969, … |
| maximal normal subgroup of | #13113907, #13113911, #13113969, … |
| maximal quotient of | #13117709, C4⋊C4×D52, #13117747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1250);