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C2×#137×#261 #16808355

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#137×#261
unambiguous semidirect productD13⋊(C4×#137)

Splittings

FittingC2×C13×#137 ⋊ C4
SylowC13 ⋊ C2×C4×#137

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×#137C4
socleC22×C13C2×C4×D4
prime radicalC2×#41×D13C22
cosocleC4×D13C25
hypercenterC2×#137#261
hypocenterC13C2×C4×#137
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1115004);