Finite Group Databasebeta

C2×#13050151 #14580852

order2624
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13050151

Splittings

SylowC41 ⋊ C2×#124

Subgroups

subgroupG/H
centerC23C22×D41
commutator, cosocleC22×C41C24
FrattiniC22C23×D41
Fitting, prime radicalC22×D4×C41C2
socleC23×C41C23
hypercenterC22×D4D41
hypocenterC41C2×#124
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C23 ◁ C22×D4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 1065);