Finite Group Databasebeta

C2×#100×#261 #16796979

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#100×#261

Splittings

FittingC2×C13×#100 ⋊ C4
SylowC13 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC22C22⋊C4×#261
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C13×#100C4
socleC22×C13C4×C22⋊C4
prime radicalC22×D4×D13C22
cosocleC2×C4×D13C24
hypercenterC2×#100#261
hypocenterC13C2×C4×#100
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#261×#453
maximal normal subgroup ofC2×#261×#453

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103628);