Finite Group DatabasebetaFinite Group Databasebeta| order | 27300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C52×C7×C13 | C22 |
| LCS | G ▷ C3×C52×C7×C13 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2730 |
Polycyclic presentation:
2^2,3,5^2,7,13|d^a=d^4,f^a=f^6,g^a=g^12,c^b=c^2,d^b=d^4,e^b=e^4,f^b=f^61755 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27300, 910);