Finite Group Databasebeta

#467×D293 #49168355

order37504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#467×D293

Splittings

Fitting#467×C293 ⋊ C2
SylowC293 ⋊ C2×#467

Subgroups

subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#467×C293C2
socleC22×C293C22×D4
prime radicalC23×D293D4
hypercenter#467D293
hypocenterC293C2×#467
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

512 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, 14080);