Finite Group Databasebeta

C2×#13050156 #14580858

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

Aliases

direct productC2×#13050156

Splittings

SylowC41 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D41
commutator, cosocleC22×C41C24
FrattiniC22C23×D41
FittingC2×C42×C41C2
socle, prime radicalC23×C41C23
hypercenterC2×C42D41
hypocenterC41C2×#125
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2624

Conjugacy classes & character table

668 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 1071);