Finite Group Databasebeta

C2×#23755715 #34092457

order19904
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#23755715

Splittings

SylowC311 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D311
commutatorC2×C311C23×C4
FrattiniC4C23×D311
Fitting, prime radicalC2×#41×C311C2
socleC22×C311C22×C4
cosocleC4×C311C24
hypercenterC2×#41D311
hypocenterC311C2×#131
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

3140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 1312);