Finite Group Databasebeta

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Dic3×C23×C31⋊C3 #38787293

order25668
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C23×C31⋊C3
unambiguous semidirect productC3⋊(C4×C23×C31⋊C3)
unambiguous semidirect product(Dic3×C31)⋊(C3×C23)
unambiguous semidirect product(Dic3×C23×C31)⋊C3

Splittings

derivedC3×C31 ⋊ C3×C4×C23
HallC3×C23×C31⋊C3 ⋊ C4
HallC23×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C4×C23
SylowC31 ⋊ C3×Dic3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23D3×C31⋊C3
commutator, hypocenterC3×C31C3×C4×C23
FrattiniC2D3×C23×C31⋊C3
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×C23×C31⋊C3C2
cosocleC2×C3×C31C2×C3×C23
LCSG ▷ C3×C31
UCSC1 ◁ C2×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8556

Conjugacy classes & character table

1794 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 40);