Finite Group Databasebeta

#41×#13097544 #38763588

order25408
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×#13097544

Splittings

Fitting#41×C397 ⋊ C4
SylowC397 ⋊ C4×#41

Subgroups

subgroupG/H
centerC4C22×#13097544
commutator, socleC2×C397C23×C4
FrattiniC2C23×#13097544
Fitting#41×C397C4
prime radical#41×D397C2
cosocleC2×D397C24
hypercenter#41#13097544
hypocenterC397C4×#41
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C4 ◁ #41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3176

Conjugacy classes & character table

1030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 1615);