Finite Group DatabasebetaFinite Group Databasebeta| order | 36368 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C2273 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #32911536 |
| commutator, hypocenter | C2273 | C16 |
| Fitting, socle, prime radical | C2×C2273 | C8 |
| cosocle | #32911534 | C2 |
| LCS | G ▷ C2273 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36368 |
Polycyclic presentation:
2^4,2273|a^2=b,b^2=c,c^2=d,e^a=e^1808,e^b=e^290,e^c=e^2272584 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36368, 52);