Finite Group Databasebeta

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C17×#1039⋊C9 #29505666

order15300
automorphism?
homologyAbelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×#1039⋊C9
unambiguous semidirect product#1039⋊(C9×C17)
unambiguous semidirect product(C17×#1039)⋊C9

Splittings

derived, SylowC52 ⋊ C4×C9×C17
HallC17×C52⋊C9 ⋊ C4
HallC17×#1039 ⋊ C9
HallC52×C17 ⋊ C4×C9
HallC52⋊C9 ⋊ C4×C17
Hall#1039 ⋊ C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17(C5⋊D5)⋊C3
commutator, hypocenterC52C4×C9×C17
FrattiniC2×C3C17×(C5⋊D5)⋊C3
Fitting, socle, prime radicalC2×C3×C52×C17C2×C3
cosocleC2×C3×C52C2×C3×C17
LCSG ▷ C52
UCSC1 ◁ C2×C3×C17

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3060

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 52);