Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C3 |
| Hall | C7×#11715913 ⋊ C2 |
| Hall | C7×D259 ⋊ C3 |
| Sylow | C72 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,37|d^a=d^6,e^a=e^36,c^b=c^2,e^b=e^26319 conjugacy classes — view the full character table.
| maximal subgroup of | #13095535⋊D7, #13095537⋊D7, D7×#13095531, … |
| maximal normal subgroup of | #13095535⋊D7, #13095537⋊D7, D7×#13095531, … |
| maximal quotient of | #36344271, C2×#24925980, #45657352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 72);