Finite Group Databasebeta

#97×D397 #38762469

order25408
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#97×D397

Splittings

Fitting#97×C397 ⋊ C2
SylowC397 ⋊ C2×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D397
commutatorC2×C397C2×C42
Fitting#97×C397C2
socleC22×C397C22×C4
prime radicalC22×D397C2×C4
cosocleC2×C4×C397C23
hypercenter#97D397
hypocenterC397C2×#97
LCSG ▷ C2×C397 ▷ C397
UCSC1 ◁ C2×C4 ◁ #97

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12704

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 496);