Finite Group Databasebeta

← Prev (#19099794) Next (#19099796) →

C3×(C5⋊D5)⋊D17 #19099795

order5100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×(C5⋊D5)⋊D17
unambiguous semidirect productD85⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C52×C17 ⋊ C22
derived, HallC52×C17 ⋊ C22×C3
HallC3×C52 ⋊ C2×D17
HallC3×C17 ⋊ D52
SylowC52 ⋊ C2×C3×D17
SylowC17 ⋊ C3×D52

Subgroups

subgroupG/H
center, hypercenterC3(C5⋊D5)⋊D17
commutator, hypocenterC52×C17C22×C3
FrattiniC1G
Fitting, socleC3×C52×C17C22
LCSG ▷ C52×C17
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×(C5⋊D5)⋊D17, C3×((C5⋊D5)⋊C3)⋊D17, C32×(C5⋊D5)⋊D17, …
maximal normal subgroup ofC9×(C5⋊D5)⋊D17, C32×(C5⋊D5)⋊D17, C3×C7×(C5⋊D5)⋊D17
maximal quotient ofC9×(C5⋊D5)⋊D17, C32×(C5⋊D5)⋊D17, C3×D85⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 98);