Finite Group Databasebeta

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C5×(C31⋊C3)⋊Dic17 #44539272

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C31⋊C3)⋊Dic17
unambiguous semidirect product(C5×Dic527)⋊C3

Splittings

derived, HallC17×C31 ⋊ C3×C4×C5
HallC5×Dic527 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC5×C17×C31 ⋊ C3×C4
HallDic527 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallC5×C31⋊C3 ⋊ Dic17
HallC5×C31 ⋊ C3×Dic17
HallC31⋊C3 ⋊ C5×Dic17
HallC5×C17 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C5×Dic17
SylowC17 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C17⋊(D31⋊C3)
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC2C5×C17⋊(D31⋊C3)
Fitting, socleC2×C5×C17×C31C2×C3
prime radicalC2×C5×C17×C31⋊C3C2
cosocleC2×C17×C31C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 29);