Finite Group Databasebeta

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C4×C17×C61⋊C5 #35208668

order20740
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C61⋊C5
unambiguous semidirect product(C4×C61)⋊(C5×C17)
unambiguous semidirect product(C4×C17×C61)⋊C5

Splittings

Fitting, HallC4×C17×C61 ⋊ C5
derived, SylowC61 ⋊ C4×C5×C17
HallC17×C61 ⋊ C4×C5
HallC4×C61 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C61⋊C5
commutator, hypocenterC61C4×C5×C17
FrattiniC2C2×C17×C61⋊C5
FittingC4×C17×C61C5
socleC2×C17×C61C2×C5
prime radicalC2×C17×C61⋊C5C2
cosocleC2×C61C2×C5×C17
LCSG ▷ C61
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4148

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20740, 2);