Finite Group DatabasebetaFinite Group Databasebeta| order | 37492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C103⋊#261) |
| unambiguous semidirect product | C103⋊(C7⋊#261) |
| Fitting, socle, derived, Hall | C7×C13×C103 ⋊ C4 |
| Hall | C13×C103 ⋊ Dic7 |
| Hall | C7×C103 ⋊ #261 |
| Sylow | C103 ⋊ C7⋊#261 |
| Hall | C7×C13 ⋊ Dic103 |
| Sylow | C13 ⋊ Dic721 |
| Sylow | C7 ⋊ C103⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C13×C103 | C4 |
| prime radical, cosocle | C7×D13×C103 | C2 |
| LCS | G ▷ C7×C13×C103 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9373 |
Polycyclic presentation:
2^2,7,13,103|a^2=b,c^a=c^6,d^a=d^5,e^a=e^102,d^b=d^122887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37492, 15);