Finite Group DatabasebetaFinite Group Databasebeta| order | 13648 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C853 ⋊ C2 |
| Sylow | C853 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D853 |
| commutator, socle, cosocle | C2×C853 | C23 |
| Fitting | Q8×C853 | C2 |
| hypercenter | Q8 | D853 |
| hypocenter | C853 | #41 |
| LCS | G ▷ C2×C853 ▷ C853 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6824 |
Polycyclic presentation:
2^4,853|c^2=d,b^a=bd,e^a=e^852,e^b=e^852,e^c=e^8522140 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #41030990, #41030992, #41030996, … |
| maximal normal subgroup of | #41030990, #41030992, #41030996, … |
| maximal quotient of | #41030927, #41030931, Q8×Dic853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13648, 41);