Finite Group Databasebeta

#41×Dic311 #34092165

order19904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic311

Splittings

SylowC311 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D311
commutatorC2×C311C23×C4
FrattiniC22C23×D311
Fitting, prime radicalC2×#41×C311C2
socle, cosocleC22×C311C24
hypercenterC2×#41D311
hypocenterC311C4×#41
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

3140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 1020);