Finite Group Databasebeta

#103×C22⋊D79 #34303697

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#103×C22⋊D79

Splittings

FittingC22×#103×C79 ⋊ C2
SylowC79 ⋊ D4×#103

Subgroups

subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×#103×C79C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
cosocleC22×C4×C79C24
hypercenterC22×#103D79
hypocenterC79D4×#103
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 184996);