Finite Group Databasebeta

#100×C22⋊D73 #33101332

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#100×C22⋊D73

Splittings

FittingC22×#100×C73 ⋊ C2
SylowC73 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC22×#100×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC2×D4×C22⋊D73C2
cosocleC22×C4×C73C24
hypercenterC22×#100D73
hypocenterC73D4×#100
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

1639 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 184916);