Finite Group Databasebeta

#416×D293 #49167277

order37504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#416×D293

Splittings

Fitting#416×C293 ⋊ C2
SylowC293 ⋊ C2×#416

Subgroups

subgroupG/H
centerC2×C4D4×D293
commutatorC4×C293C23×C4
FrattiniC2×C4C23×D293
Fitting#416×C293C2
socleC22×C293C22×D4
prime radicalC2×#41×D293C2
cosocleC2×C4×C293C24
hypercenter#416D293
hypocenterC293C2×#416
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

4144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 13002);