Finite Group Databasebeta

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C4×C5×C103⋊C17 #46855898

order35020
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C103⋊C17
unambiguous semidirect product(C4×C103)⋊(C5×C17)
unambiguous semidirect product(C4×C5×C103)⋊C17

Splittings

Fitting, HallC4×C5×C103 ⋊ C17
derived, SylowC103 ⋊ C4×C5×C17
HallC5×C103 ⋊ C4×C17
HallC4×C103 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C5C103⋊C17
commutator, hypocenterC103C4×C5×C17
FrattiniC2C2×C5×C103⋊C17
FittingC4×C5×C103C17
socleC2×C5×C103C2×C17
prime radicalC2×C5×C103⋊C17C2
cosocleC2×C103C2×C5×C17
LCSG ▷ C103
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35020, 2);