Finite Group Databasebeta

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C31×Dic65⋊C3 #37563755

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C31)

Splittings

derived, HallC5×C13 ⋊ C3×C4×C31
HallC31×Dic65 ⋊ C3
HallC5×C31×C13⋊C3 ⋊ C4
HallC5×C13×C31 ⋊ C3×C4
HallC31×C13⋊C3 ⋊ Dic5
HallC13×C31 ⋊ C3×Dic5
HallDic65 ⋊ C3×C31
HallC5×C13⋊C3 ⋊ C4×C31
HallC5×C31 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ Dic5×C31
SylowC13 ⋊ C3×Dic5×C31
SylowC5 ⋊ C31×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C31C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C31
FrattiniC2C31×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C13×C31C2×C3
prime radicalC2×C5×C31×C13⋊C3C2
cosocleC2×C5×C13C2×C3×C31
LCSG ▷ C5×C13
UCSC1 ◁ C2×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 54);