Finite Group Databasebeta

← Prev (#49178455) Next (#49178457) →

C3×C11⋊C5×Dic57 #49178456

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×Dic57
unambiguous semidirect productC3⋊(C3×C11⋊C5×Dic19)
unambiguous semidirect product(C3×C11×Dic57)⋊C5

Splittings

derivedC3×C11×C19 ⋊ C3×C4×C5
HallC32×C19×C11⋊C5 ⋊ C4
HallC3×C11×Dic57 ⋊ C5
HallC32×C11×C19 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C3×Dic3
HallC32×C11⋊C5 ⋊ Dic19
HallC11×C19 ⋊ C3×C5×Dic3
HallC32×C19 ⋊ C4×C11⋊C5
HallC32×C11 ⋊ C5×Dic19
SylowC19 ⋊ C3×Dic3×C11⋊C5
SylowC11 ⋊ C3×C5×Dic57
SylowC32 ⋊ C11⋊C5×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×D57
commutator, hypocenterC3×C11×C19C3×C4×C5
FrattiniC2C3×C11⋊C5×D57
Fitting, socleC2×C32×C11×C19C2×C5
prime radicalC2×C32×C19×C11⋊C5C2
cosocleC2×C3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2508

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 165);