Finite Group Databasebeta

C22×Dic152 #14576748

order2432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic152

Splittings

SylowC19 ⋊ C22×Q32

Subgroups

subgroupG/H
centerC23D152
commutator, cosocleC8×C19C24
FrattiniC8C23×D19
FittingC22×C16×C19C2
socle, prime radicalC23×C19D8
hypercenterC22×C16D19
hypocenterC19C22×Q32
LCSG ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17623);