Finite Group Databasebeta

C22×#21463312 #44537485

order31424
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#21463312

Splittings

SylowC491 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D491
commutatorC2×C491C23×C4
FrattiniC4C23×D491
FittingC23×C4×C491C2
socleC23×C491C2×C4
prime radicalC24×C491C4
cosocleC4×C491C24
hypercenterC23×C4D491
hypocenterC491C22×M16
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

7880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 1309);