Finite Group Databasebeta

#419×D197 #38751215

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#419×D197

Splittings

Fitting#419×C197 ⋊ C2
SylowC197 ⋊ C2×#419

Subgroups

subgroupG/H
centerC22C2×D4×D197
commutatorC4×C197C23×C4
FrattiniC2×C4C23×D197
Fitting#419×C197C2
socleC22×C197C22×D4
prime radicalC23×D197D4
cosocleC2×C4×C197C24
hypercenter#419D197
hypocenterC197C2×#419
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 13013);