Finite Group Databasebeta

C2×#13050103 #14580750

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

Aliases

direct productC2×#13050103

Splittings

FittingC2×C16×C41 ⋊ C2
SylowC41 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D41
commutatorC2×C41C22×C8
FrattiniC8C22×D41
FittingC2×C16×C41C2
socleC22×C41C2×C8
prime radicalC22×D41C8
cosocleC8×C41C23
hypercenterC2×C16D41
hypocenterC41C2×M32
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C8 ◁ C2×C16

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, 963);