Finite Group Databasebeta

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C2×#135×#261 #16808349

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

Aliases

direct productC2×#135×#261
unambiguous semidirect productD13⋊(C4×#135)

Splittings

FittingC2×C13×#135 ⋊ C4
SylowC13 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC2×C13×#135C4
socleC22×C13C2×C4×D4
prime radicalC2×D13×#135C2
cosocleC4×D13C25
hypercenterC2×#135#261
hypocenterC13C2×C4×#135
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114998);