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C17×(C31⋊C3)⋊Dic5 #44539274

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C31⋊C3)⋊Dic5
unambiguous semidirect product(C31⋊C3)⋊(C17×Dic5)
unambiguous semidirect productDic155⋊(C3×C17)
unambiguous semidirect product(C17×Dic155)⋊C3

Splittings

derived, HallC5×C31 ⋊ C3×C4×C17
HallC17×Dic155 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC5×C17×C31 ⋊ C3×C4
HallC17×C31⋊C3 ⋊ Dic5
HallDic155 ⋊ C3×C17
HallC17×C31 ⋊ C3×Dic5
HallC5×C31⋊C3 ⋊ C4×C17
HallC31⋊C3 ⋊ C17×Dic5
HallC5×C17 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C17×Dic5
SylowC5 ⋊ C17×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C17C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C3×C4×C17
FrattiniC2C17×C5⋊(D31⋊C3)
Fitting, socleC2×C5×C17×C31C2×C3
prime radicalC2×C5×C17×C31⋊C3C2
cosocleC2×C5×C31C2×C3×C17
LCSG ▷ C5×C31
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 31);