Finite Group Databasebeta

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C137×(C19⋊C3)⋊C4 #44530323

order31236
automorphism?
homologyAbelianization (H1) = C3×C4×C137 · Schur multiplier (H2) = C1

Aliases

direct productC137×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C137)
unambiguous semidirect productDic19⋊(C3×C137)
unambiguous semidirect product(Dic19×C137)⋊C3

Splittings

derived, SylowC19 ⋊ C3×C4×C137
HallDic19×C137 ⋊ C3
HallC19⋊C3×C137 ⋊ C4
HallC19×C137 ⋊ C3×C4
HallDic19 ⋊ C3×C137
HallC19⋊C3 ⋊ C4×C137

Subgroups

subgroupG/H
center, hypercenterC2×C137D19⋊C3
commutator, hypocenterC19C3×C4×C137
FrattiniC2D19⋊C3×C137
Fitting, socleC2×C19×C137C2×C3
prime radicalC2×C19⋊C3×C137C2
cosocleC2×C19C2×C3×C137
LCSG ▷ C19
UCSC1 ◁ C2×C137

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10412

Conjugacy classes & character table

2466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31236, 11);