Finite Group Databasebeta

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Dic2665⋊C3 #44544305

order31980
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productDic2665⋊C3

Splittings

derived, HallC5×C13×C41 ⋊ C3×C4
HallDic2665 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
HallC13⋊C3×C41 ⋊ Dic5
HallC13×C41 ⋊ C3×Dic5
HallC5×C41 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ Dic41
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ Dic65⋊C3
HallC13⋊C3 ⋊ Dic205
SylowC13 ⋊ C3×Dic205
SylowC5 ⋊ Dic533⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C5⋊((C13⋊C3)⋊D41)
commutator, hypocenterC5×C13×C41C3×C4
Fitting, socle, cosocleC2×C5×C13×C41C2×C3
prime radicalC2×C5×C13⋊C3×C41C2
LCSG ▷ C5×C13×C41
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10660

Polycyclic presentation:

2,3,5,13,41,2|a^2=f,c^a=c^4,d^a=d^12,e^a=e^40,d^b=d^3

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 33);