Finite Group DatabasebetaFinite Group Databasebeta| order | 2116 |
| isoclinism | isoclinic class of #14523747 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C232 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C232 | C4 |
| prime radical, cosocle | C23⋊D23 | C2 |
| LCS | G ▷ C232 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 46 |
Polycyclic presentation:
2^2,23^2|a^2=b,c^a=c^11d^12,d^a=c^9d^12,c^b=c^22,d^b=d^22136 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523747, C7⋊#14523747, #34039976, … |
| maximal normal subgroup of | C7×#14523747, #14523747⋊C11, C11×#14523747, … |
| maximal quotient of | C7×#14523747, C7⋊#14523747, #34039976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2116, 10);