Finite Group Databasebeta

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C5×C19⋊C3×Dic33 #49178472

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

Aliases

direct productC5×C19⋊C3×Dic33
unambiguous semidirect productC3⋊(C5×Dic11×C19⋊C3)
unambiguous semidirect product(C5×C19×Dic33)⋊C3

Splittings

derivedC3×C11×C19 ⋊ C3×C4×C5
HallC3×C5×C11×C19⋊C3 ⋊ C4
HallC3×C11×C19⋊C3 ⋊ C4×C5
HallC5×C11×C19 ⋊ C3×Dic3
HallC3×C5×C19⋊C3 ⋊ Dic11
HallC11×C19 ⋊ C3×C5×Dic3
HallC3×C19⋊C3 ⋊ C5×Dic11
HallC5×C19 ⋊ C3×Dic33
HallC5×C11 ⋊ Dic3×C19⋊C3
SylowC19 ⋊ C3×C5×Dic33
SylowC11 ⋊ C5×Dic3×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C19⋊C3×D33
commutator, hypocenterC3×C11×C19C3×C4×C5
FrattiniC2C5×C19⋊C3×D33
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C11×C19⋊C3C2
cosocleC2×C3×C11×C19C2×C3×C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C2×C5

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) = 12540

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 181);