Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ #518 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#261 |
| commutator, socle | C2×C13 | C23×C4 |
| Fitting | C2×D4×C13 | C4 |
| prime radical | C2×D4×D13 | C2 |
| cosocle | C2×D13 | C24 |
| hypercenter | C2×D4 | #261 |
| hypocenter | C13 | #518 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^6,13|a^2=e,d^a=df,g^a=g^8,c^b=cf,g^e=g^1264 conjugacy classes — view the full character table.
| maximal subgroup of | #13130791, #13130807, #13130841, … |
| maximal normal subgroup of | #13130791, #13130807, #13130841, … |
| maximal quotient of | #13131272, #13131274, #13131275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1589);