Finite Group Databasebeta

#103×C22⋊D17 #17049752

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#103×C22⋊D17

Splittings

FittingC22×C17×#103 ⋊ C2
SylowC17 ⋊ D4×#103

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#103C2
socleC23×C17C22×D4
prime radicalC22×C22⋊D17D4
cosocleC22×C4×C17C24
hypercenterC22×#103D17
hypocenterC17D4×#103
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 184996);