Finite Group Databasebeta

C22×C22⋊#64408 #17989648

order4672
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊#64408
unambiguous semidirect productD73⋊(C2×C22⋊C4)
unambiguous semidirect product(C2×#64408)⋊C23

Splittings

FittingC24×C73 ⋊ C4
SylowC73 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×#64408
commutatorC2×C73C23×C4
FrattiniC2C23×#64408
FittingC24×C73C4
socleC23×C73C2×C4
prime radicalC24×D73C2
cosocleC2×D73C24
hypercenterC24#64408
hypocenterC73C22×C22⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 1610);