Finite Group Databasebeta

C2×#23755625 #34091671

order19904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#23755625

Splittings

SylowC311 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic311
commutatorC22×C311C22×C4
FrattiniC2×C4C22×D311
Fitting, prime radicalC22×D4×C311C2
socleC22×C311C22⋊C4
cosocleC2×C4×C311C23
hypercenterC22×D4D311
hypocenterC311C2×#100
LCSG ▷ C22×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4976

Conjugacy classes & character table

3122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 526);