Finite Group Databasebeta

#347×Dic59 #28503515

order15104
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C42

Aliases

direct product#347×Dic59

Splittings

SylowC59 ⋊ C4×#347

Subgroups

subgroupG/H
centerC2×C4C42×D59
commutatorC4×C59C43
FrattiniC22×C8C22×D59
FittingC2×C59×#347C2
socleC22×C59C2×#97
prime radicalC23×C59C2×M16
cosocleC22×C8×C59C23
hypercenterC2×#347D59
hypocenterC59C4×#347
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#347

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 84394);