Finite Group Databasebeta

C2×#23755640 #34091725

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

Aliases

direct productC2×#23755640

Splittings

SylowC311 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23D1244
commutatorC4×C311C22×C4
FrattiniC2×C4C22×D311
FittingC22×C8×C311C2
socle, prime radicalC23×C311D4
cosocleC2×C4×C311C23
hypercenterC22×C8D311
hypocenterC311C2×#106
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19904

Conjugacy classes & character table

4988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 580);