Finite Group Databasebeta

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C17×C3⋊(#1043⋊C3) #29505898

order15300
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊(#1043⋊C3)
unambiguous semidirect productC3⋊(C17×#1043⋊C3)
unambiguous semidirect product(C3⋊#1043)⋊(C3×C17)
unambiguous semidirect product(C17×C3⋊#1043)⋊C3

Splittings

Fitting, socleC3×C52×C17 ⋊ C3×C4
derivedC3×C52 ⋊ C3×C4×C17
HallC3×C17×C52⋊C3 ⋊ C4
HallC52×C17 ⋊ C3×Dic3
HallC3×C52⋊C3 ⋊ C4×C17
SylowC52 ⋊ C3×Dic3×C17

Subgroups

subgroupG/H
center, hypercenterC17C3⋊(#1043⋊C3)
commutator, hypocenterC3×C52C3×C4×C17
FrattiniC1G
Fitting, socleC3×C52×C17C3×C4
prime radicalC3×C17×(C5⋊D5)⋊C3C2
cosocleC3×C5⋊D5C2×C3×C17
LCSG ▷ C3×C52
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 765

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 284);