Finite Group Databasebeta

#462×D197 #38752146

order25216
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#462×D197

Splittings

Fitting#462×C197 ⋊ C2
SylowC197 ⋊ C2×#462

Subgroups

subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
Fitting#462×C197C2
socleC22×C197C22×D4
prime radicalC22×D197C2×D4
hypercenter#462D197
hypocenterC197C2×#462
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ #462

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13944);