Finite Group Databasebeta

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C19⋊C3×Dic165 #49178476

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

Aliases

direct productC19⋊C3×Dic165
unambiguous semidirect productC3⋊(C19⋊C3×Dic55)
unambiguous semidirect productC11⋊(C19⋊C3×Dic15)
unambiguous semidirect product(C19×Dic165)⋊C3

Splittings

derivedC3×C5×C11×C19 ⋊ C3×C4
HallC3×C5×C11×C19⋊C3 ⋊ C4
HallC3×C11×C19⋊C3 ⋊ Dic5
HallC5×C11×C19 ⋊ C3×Dic3
HallC3×C5×C19⋊C3 ⋊ Dic11
HallC11×C19 ⋊ C3×Dic15
HallC3×C19⋊C3 ⋊ Dic55
HallC5×C19 ⋊ C3×Dic33
HallC5×C11 ⋊ Dic3×C19⋊C3
SylowC19 ⋊ C3×Dic165
SylowC11 ⋊ C19⋊C3×Dic15
SylowC5 ⋊ C19⋊C3×Dic33

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C19⋊C3×D165
commutator, hypocenterC3×C5×C11×C19C3×C4
Fitting, socle, cosocleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C11×C19⋊C3C2
LCSG ▷ C3×C5×C11×C19
UCSC1 ◁ C2

112 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 51 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

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 185);