Finite Group Databasebeta

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C2×C5×C9×D5×C17 #29505829

order15300
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D5×C17
unambiguous semidirect productC5⋊(C22×C5×C9×C17)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C9×C17)

Splittings

FittingC2×C52×C9×C17 ⋊ C2
derivedC5 ⋊ C22×C5×C9×C17
HallC52×C9×C17 ⋊ C22
HallC52×C17 ⋊ C22×C9
HallC52×C9 ⋊ C22×C17
SylowC52 ⋊ C22×C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C17D5
commutator, hypocenterC5C22×C5×C9×C17
FrattiniC3C2×C3×C5×D5×C17
FittingC2×C52×C9×C17C2
socleC2×C3×C52×C17C2×C3
prime radicalC2×C3×C5×D5×C17C3
cosocleC3×C5C22×C3×C5×C17
LCSG ▷ C5
UCSC1 ◁ C2×C5×C9×C17

144 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 3060

Conjugacy classes & character table

6120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 215);