Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #3866 |
| commutator, hypocenter | C37 | C64 |
| Fitting | C16×C37 | C4 |
| socle, prime radical | C2×C37 | C32 |
| cosocle | #11924442 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 2368 |
Polycyclic presentation:
2^6,37|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^31,g^b=g^36208 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14558372, D37⋊C64, #18009765, … |
| maximal normal subgroup of | C2×#14558372, D37⋊C64, #18009765, … |
| maximal quotient of | #18009411, C2×#14558372 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 1388);