Finite Group Databasebeta

#97×D457 #44416724

order29248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#97×D457

Splittings

Fitting#97×C457 ⋊ C2
SylowC457 ⋊ C2×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D457
commutatorC2×C457C2×C42
Fitting#97×C457C2
socleC22×C457C22×C4
prime radicalC22×D457C2×C4
cosocleC2×C4×C457C23
hypercenter#97D457
hypocenterC457C2×#97
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C2×C4 ◁ #97

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 496);