Finite Group Databasebeta

C2×#26039940 #37526435

order22976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#26039940

Splittings

SylowC359 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23D1436
commutatorC4×C359C22×C4
FrattiniC2×C4C22×D359
FittingC22×C8×C359C2
socle, prime radicalC23×C359D4
cosocleC2×C4×C359C23
hypercenterC22×C8D359
hypocenterC359C2×#103
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22976

Conjugacy classes & character table

5756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 541);