Finite Group Databasebeta

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C3×C5×Dic5×C19⋊C3 #30685648

order17100
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×Dic5×C19⋊C3
unambiguous semidirect product(C19×Dic5)⋊(C32×C5)
unambiguous semidirect product(C3×C19×Dic5)⋊(C3×C5)
unambiguous semidirect product(C5×C19×Dic5)⋊C32
unambiguous semidirect product(C3×C5×C19×Dic5)⋊C3

Splittings

derivedC5×C19 ⋊ C32×C4×C5
HallC3×C52×C19⋊C3 ⋊ C4
HallC5×C19×Dic5 ⋊ C32
HallC52×C19 ⋊ C32×C4
SylowC52 ⋊ C3×C4×C19⋊C3
SylowC19 ⋊ C32×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D5×C19⋊C3
commutator, hypocenterC5×C19C32×C4×C5
FrattiniC2C3×C5×D5×C19⋊C3
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C52×C19⋊C3C2
cosocleC2×C5×C19C2×C32×C5
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C5

192 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 1140

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 285);