Finite Group Databasebeta

#97×D419 #41000308

order26816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#97×D419

Splittings

Fitting#97×C419 ⋊ C2
SylowC419 ⋊ C2×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D419
commutatorC2×C419C2×C42
Fitting#97×C419C2
socleC22×C419C22×C4
prime radicalC22×D419C2×C4
cosocleC2×C4×C419C23
hypercenter#97D419
hypocenterC419C2×#97
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C2×C4 ◁ #97

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

4220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 496);