Finite Group Databasebeta

#419×D293 #49167288

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

Aliases

direct product#419×D293

Splittings

Fitting#419×C293 ⋊ C2
SylowC293 ⋊ C2×#419

Subgroups

subgroupG/H
centerC22C2×D4×D293
commutatorC4×C293C23×C4
FrattiniC2×C4C23×D293
Fitting#419×C293C2
socleC22×C293C22×D4
prime radicalC23×D293D4
cosocleC2×C4×C293C24
hypercenter#419D293
hypocenterC293C2×#419
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

3256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 13013);