Finite Group Databasebeta

#413×D197 #38751183

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

Aliases

direct product#413×D197

Splittings

Fitting#413×C197 ⋊ C2
SylowC197 ⋊ C2×#413

Subgroups

subgroupG/H
centerC4C22⋊C4×D197
commutatorC22×C197C23×C4
FrattiniC2×C4C23×D197
Fitting#413×C197C2
socleC2×C197C22×C22⋊C4
prime radicalC2×#41×D197C2
cosocleC2×C4×C197C24
hypercenter#413D197
hypocenterC197C2×#413
LCSG ▷ C22×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3152

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, 12981);