Finite Group Databasebeta

#103×C22⋊D59 #28604117

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#103×C22⋊D59

Splittings

FittingC22×#103×C59 ⋊ C2
SylowC59 ⋊ D4×#103

Subgroups

subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC22×#103×C59C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
cosocleC22×C4×C59C24
hypercenterC22×#103D59
hypocenterC59D4×#103
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 184996);