Finite Group Databasebeta

C2×#26039958 #37526866

order22976
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#26039958

Splittings

FittingC2×Q16×C359 ⋊ C2
SylowC359 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#19153326
commutator, cosocleC8×C359C23
FrattiniC8C22×D359
FittingC2×Q16×C359C2
socleC22×C359D8
prime radicalC2×D2872C2
hypercenterC2×Q16D359
hypocenterC359C2×SD32
LCSG ▷ C8×C359 ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

2528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 972);