Finite Group Databasebeta

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C3×C5×(C19⋊C3)⋊Dic5 #30685647

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

Aliases

direct productC3×C5×(C19⋊C3)⋊Dic5
unambiguous semidirect product(C19⋊C3)⋊(C3×C5×Dic5)
unambiguous semidirect productDic95⋊(C32×C5)
unambiguous semidirect product(C3×Dic95)⋊(C3×C5)
unambiguous semidirect product(C5×Dic95)⋊C32
unambiguous semidirect product(C3×C5×Dic95)⋊C3

Splittings

derivedC5×C19 ⋊ C32×C4×C5
HallC3×C52×C19⋊C3 ⋊ C4
HallC5×Dic95 ⋊ C32
HallC52×C19 ⋊ C32×C4
HallC3×C19⋊C3 ⋊ C5×Dic5
SylowC52 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C32×C4×C5
FrattiniC2C3×C5×C5⋊(D19⋊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 76 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 76 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 284);