Finite Group Databasebeta

C22×C22⋊#13063703 #36375205

order22336
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×C22⋊#13063703
unambiguous semidirect productD349⋊(C2×C22⋊C4)
unambiguous semidirect product(C2×#13063703)⋊C23

Splittings

FittingC24×C349 ⋊ C4
SylowC349 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×#13063703
commutatorC2×C349C23×C4
FrattiniC2C23×#13063703
FittingC24×C349C4
socleC23×C349C2×C4
prime radicalC24×D349C2
cosocleC2×D349C24
hypercenterC24#13063703
hypocenterC349C22×C22⋊C4
LCSG ▷ C2×C349 ▷ C349
UCSC1 ◁ C23 ◁ C24

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5584

Conjugacy classes & character table

1432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22336, 1610);