Finite Group Databasebeta

#339×D197 #38742416

order25216
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D197

Splittings

Fitting#339×C197 ⋊ C2
SylowC197 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D197
commutatorC4×C197C2×C42
FrattiniC22×C4C22×D197
Fitting#339×C197C2
socleC22×C197C2×C22⋊C4
prime radicalC23×D197D4
cosocleC22×C4×C197C23
hypercenter#339D197
hypocenterC197C2×#339
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 4214);