Finite Group Databasebeta

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C17×Dic101⋊C5 #46805113

order34340
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic101⋊C5
unambiguous semidirect productDic101⋊(C5×C17)
unambiguous semidirect product(C17×Dic101)⋊C5

Splittings

derived, SylowC101 ⋊ C4×C5×C17
HallC17×C101⋊C5 ⋊ C4
HallC17×Dic101 ⋊ C5
HallC17×C101 ⋊ C4×C5
HallC101⋊C5 ⋊ C4×C17
HallDic101 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D101⋊C5
commutator, hypocenterC101C4×C5×C17
FrattiniC2C17×D101⋊C5
Fitting, socleC2×C17×C101C2×C5
prime radicalC2×C17×C101⋊C5C2
cosocleC2×C101C2×C5×C17
LCSG ▷ C101
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6868

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34340, 10);