Finite Group Databasebeta

C2×#26039933 #37526422

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

Aliases

direct productC2×#26039933

Splittings

SylowC359 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22(C2×D359)⋊C4
commutatorC22×C359C22×C4
FrattiniC2×C4C22×D359
FittingC2×M16×C359C2
socleC22×C359C22⋊C4
prime radicalC23×C359C2×C4
cosocleC2×C4×C359C23
hypercenterC2×M16D359
hypocenterC359C2×#101
LCSG ▷ C22×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

3602 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 528);