Finite Group Databasebeta

#349×Dic59 #28503731

order15104
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#349×Dic59

Splittings

SylowC59 ⋊ C4×#349

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC22×C59C2×C4×C8
FrattiniC22×C8C22×D59
FittingC2×C59×#349C2
socleC22×C59C2×C22⋊C8
prime radicalC24×C59C2×C8
cosocleC22×C8×C59C23
hypercenterC2×#349D59
hypocenterC59C4×#349
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

522 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, 84610);