Finite Group Databasebeta

C22×Dic1964 #44537502

order31424
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1964

Splittings

SylowC491 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1964
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingC22×C8×C491C2
socle, prime radicalC23×C491D4
hypercenterC22×C8D491
hypocenterC491C22×Q16
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31424

Conjugacy classes & character table

7868 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 1326);