Finite Group DatabasebetaFinite Group Databasebeta| order | 2368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4⋊C8×C37 ⋊ C2 |
| Sylow | C37 ⋊ #433 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1184 |
Polycyclic presentation:
2^6,37|a^2=e,c^2=d,e^2=f,b^a=bd,c^b=cf,g^b=g^36,g^c=g^36388 conjugacy classes — view the full character table.
| maximal subgroup of | #433×D37, C2×#14557593, #18003230, … |
| maximal normal subgroup of | #433×D37, C2×#14557593, #18003230, … |
| maximal quotient of | #17994346, #17994361, #17994455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2368, 609);