Finite Group Databasebeta

C2×#13050104 #14580751

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

Aliases

direct productC2×#13050104

Splittings

SylowC41 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D41
commutatorC2×C41C22×C8
FrattiniC8C22×D41
FittingC22×C8×C41C2
socleC22×C41C2×C8
prime radicalC23×C41C8
cosocleC8×C41C23
hypercenterC22×C8D41
hypocenterC41C2×M32
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 964);