Finite Group Databasebeta

C2×#13050239 #14581393

order2624
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13050239

Splittings

SylowC41 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C4C2×#4223
commutatorC2×C41C22×C8
FrattiniC4C22×#4223
FittingC2×C8×C41C4
socleC22×C41C2×C8
prime radicalC22×D41C8
cosocle#66491C23
hypercenterC2×C8#4223
hypocenterC41C2×M32
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C4 ◁ C2×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 1606);