Finite Group Databasebeta

#100×C22⋊D79 #34303617

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

Aliases

direct product#100×C22⋊D79

Splittings

FittingC22×#100×C79 ⋊ C2
SylowC79 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D79
commutatorC23×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×#100×C79C2
socleC22×C79C22×C22⋊C4
prime radicalC2×D4×C22⋊D79C2
cosocleC22×C4×C79C24
hypercenterC22×#100D79
hypocenterC79D4×#100
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

1771 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 184916);