Finite Group Databasebeta

C2×#23755619 #34091643

order19904
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#23755619

Splittings

SylowC311 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D311
commutatorC2×C311C2×C42
FrattiniC2×C4C22×D311
FittingC2×C42×C311C2
socle, prime radicalC23×C311C2×C4
cosocleC2×C4×C311C23
hypercenterC2×C42D311
hypocenterC311C2×#97
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C22×C4 ◁ C2×C42

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19904

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, 498);