Finite Group Databasebeta

C2×#23755665 #34092148

order19904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#23755665

Splittings

FittingC2×C42×C311 ⋊ C2
SylowC311 ⋊ C2×#117

Subgroups

subgroupG/H
centerC22×C4C2×D311
commutatorC2×C311C23×C4
FrattiniC22C23×D311
FittingC2×C42×C311C2
socleC23×C311C23
prime radicalC23×D311C22
cosocleC22×C311C24
hypercenterC2×C42D311
hypocenterC311C2×#117
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C22×C4 ◁ C2×C42

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

5000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 1003);