Finite Group Databasebeta

C22×Dic232 #16832605

order3712
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic232

Splittings

SylowC29 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23D232
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC22×C16×C29C2
socle, prime radicalC23×C29D8
hypercenterC22×C16D29
hypocenterC29C22×Q32
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 17623);