Finite Group Databasebeta

#101×D397 #38762500

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D397

Splittings

Fitting#101×C397 ⋊ C2
SylowC397 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D397
commutatorC22×C397C22×C4
FrattiniC2×C4C22×D397
Fitting#101×C397C2
socleC2×C397C2×C22⋊C4
prime radicalC22×D397C2×C4
cosocleC2×C4×C397C23
hypercenter#101D397
hypocenterC397C2×#101
LCSG ▷ C22×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

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(25408, 527);