Finite Group Databasebeta

#417×D197 #38751220

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

Aliases

direct product#417×D197

Splittings

Fitting#417×C197 ⋊ C2
SylowC197 ⋊ C2×#417

Subgroups

subgroupG/H
centerC22C2×D4×D197
commutatorC4×C197C23×C4
FrattiniC2×C4C23×D197
Fitting#417×C197C2
socleC22×C197C22×D4
prime radicalC2×#41×D197C2
cosocleC2×C4×C197C24
hypercenter#417D197
hypocenterC197C2×#417
LCSG ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

816 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, 13018);