Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C22×C32 |
| Hall | ΓL(1,𝔽8)×#63270 ⋊ C22 |
| Hall | D13×C7⋊D7 ⋊ C32 |
| Sylow | C72 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C22×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
280 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 273 |
Polycyclic presentation:
2^2,3^2,7^2,13|g^a=g^12,e^b=e^6,f^b=f^6,f^c=f^2,g^c=g^3,e^d=e^296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 855);