Finite Group Databasebeta

← Prev (#49178486) Next (#49178488) →

C3×Dic3135 #49178487

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

Aliases

direct productC3×Dic3135
unambiguous semidirect productC3⋊(C3×Dic1045)
unambiguous semidirect productC11⋊(C3×Dic285)

Splittings

derivedC3×C5×C11×C19 ⋊ C3×C4
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ C3×Dic3
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3×Dic15
HallC32×C19 ⋊ Dic55
HallC32×C11 ⋊ Dic95
HallC5×C19 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×Dic57
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C3×Dic165
SylowC11 ⋊ C3×Dic285
SylowC32 ⋊ Dic1045
SylowC5 ⋊ C3×Dic627

Subgroups

subgroupG/H
center, hypercenterC2×C3D3135
commutator, hypocenterC3×C5×C11×C19C3×C4
FrattiniC2C3×D3135
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C3×C5×C11×C19C2×C3
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 12540

Conjugacy classes & character table

9414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 196);