Finite Group Databasebeta

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C5×Dic103⋊C17 #46855906

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

Aliases

direct productC5×Dic103⋊C17
unambiguous semidirect productDic103⋊(C5×C17)
unambiguous semidirect product(C103⋊C17)⋊(C4×C5)
unambiguous semidirect product(C5×Dic103)⋊C17

Splittings

derived, SylowC103 ⋊ C4×C5×C17
HallC5×C103⋊C17 ⋊ C4
HallC5×Dic103 ⋊ C17
HallC103⋊C17 ⋊ C4×C5
HallC5×C103 ⋊ C4×C17
HallDic103 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5D103⋊C17
commutator, hypocenterC103C4×C5×C17
FrattiniC2C5×D103⋊C17
Fitting, socleC2×C5×C103C2×C17
prime radicalC2×C5×C103⋊C17C2
cosocleC2×C103C2×C5×C17
LCSG ▷ C103
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35020, 10);