Finite Group Databasebeta

#520×D197 #38755904

order25216
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#520×D197

Splittings

Fitting#520×C197 ⋊ C2
SylowC197 ⋊ C2×#520

Subgroups

subgroupG/H
center, FrattiniC22C24×D197
commutatorC2×C197C24×C4
Fitting#520×C197C2
socle, cosocleC22×C197C25
prime radicalC2×#41×D197C2
hypercenter#520D197
hypocenterC197C2×#520
LCSG ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ #520

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

Conjugacy classes & character table

3400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 17702);