Finite Group Databasebeta

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C101×Dic13⋊C3 #30628736

order15756
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C101 · Schur multiplier (H2) = C1

Aliases

direct productC101×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C101)
unambiguous semidirect product(Dic13×C101)⋊C3

Splittings

derived, SylowC13 ⋊ C3×C4×C101
HallDic13×C101 ⋊ C3
HallC13⋊C3×C101 ⋊ C4
HallC13×C101 ⋊ C3×C4
HallDic13 ⋊ C3×C101
HallC13⋊C3 ⋊ C4×C101

Subgroups

subgroupG/H
center, hypercenterC2×C101D13⋊C3
commutator, hypocenterC13C3×C4×C101
FrattiniC2D13⋊C3×C101
Fitting, socleC2×C13×C101C2×C3
prime radicalC2×C13⋊C3×C101C2
cosocleC2×C13C2×C3×C101
LCSG ▷ C13
UCSC1 ◁ C2×C101

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5252

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15756, 11);