Finite Group Databasebeta

C22×#11745146 #16832587

order3712
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11745146

Splittings

FittingC22×C16×C29 ⋊ C2
SylowC29 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D29
commutatorC2×C29C23×C8
FrattiniC8C23×D29
FittingC22×C16×C29C2
socleC23×C29C2×C8
prime radicalC23×D29C8
cosocleC8×C29C24
hypercenterC22×C16D29
hypocenterC29C22×M32
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C8 ◁ C22×C16

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17605);