Finite Group Databasebeta

#41×Dic491 #44537196

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

Aliases

direct product#41×Dic491

Splittings

SylowC491 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D491
commutatorC2×C491C23×C4
FrattiniC22C23×D491
Fitting, prime radicalC2×#41×C491C2
socle, cosocleC22×C491C24
hypercenterC2×#41D491
hypocenterC491C4×#41
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

4940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 1020);