Finite Group Databasebeta

C2×#23755629 #34091681

order19904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#23755629

Splittings

SylowC311 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D311
commutatorC4×C311C22×C4
FrattiniC2×C4C22×D311
Fitting, prime radicalC22×D4×C311C2
socleC23×C311D4
cosocleC2×C4×C311C23
hypercenterC22×D4D311
hypocenterC311C2×#102
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

3128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 536);