Finite Group Databasebeta

C2×Dic2872 #37526871

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

Aliases

direct productC2×Dic2872

Splittings

SylowC359 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D2872
commutator, cosocleC8×C359C23
FrattiniC8C22×D359
FittingC2×C16×C359C2
socle, prime radicalC22×C359D8
hypercenterC2×C16D359
hypocenterC359C2×Q32
LCSG ▷ C8×C359 ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

5750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 977);