Finite Group Databasebeta

#388×D197 #38745140

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#388×D197

Splittings

Fitting#388×C197 ⋊ C2
SylowC197 ⋊ C2×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×D197
commutatorC22×C197C23×C4
Fitting#388×C197C2
socle, cosocleC23×C197C24
prime radicalC24×D197C22
hypercenter#388D197
hypocenterC197C2×#388
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ #388

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6304

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, 6938);