Finite Group Databasebeta

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C149×Dic13⋊C3 #37551260

order23244
automorphism?
homologyAbelianization (H1) = C3×C4×C149 · Schur multiplier (H2) = C1

Aliases

direct productC149×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C149)
unambiguous semidirect product(Dic13×C149)⋊C3

Splittings

derived, SylowC13 ⋊ C3×C4×C149
HallDic13×C149 ⋊ C3
HallC13⋊C3×C149 ⋊ C4
HallC13×C149 ⋊ C3×C4
HallDic13 ⋊ C3×C149
HallC13⋊C3 ⋊ C4×C149

Subgroups

subgroupG/H
center, hypercenterC2×C149D13⋊C3
commutator, hypocenterC13C3×C4×C149
FrattiniC2D13⋊C3×C149
Fitting, socleC2×C13×C149C2×C3
prime radicalC2×C13⋊C3×C149C2
cosocleC2×C13C2×C3×C149
LCSG ▷ C13
UCSC1 ◁ C2×C149

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7748

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23244, 11);