Finite Group Databasebeta

C2×C22⋊#66493 #14581303

order2624
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#66493

Splittings

SylowC41 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#4223
commutatorC2×C41C22×C8
FrattiniC22C22×#4223
Fitting, prime radicalC24×C41C4
socleC23×C41C2×C4
cosocleC2×Dic41C23
hypercenterC24#4223
hypocenterC41C2×C22⋊C8
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C23 ◁ C24

202 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, 1516);