Finite Group Databasebeta

C22×#19097298 #34092453

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

Aliases

direct productC22×#19097298

Splittings

FittingC22×C8×C311 ⋊ C2
SylowC311 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D311
commutatorC2×C311C23×C4
FrattiniC4C23×D311
FittingC22×C8×C311C2
socleC23×C311C2×C4
prime radicalC23×D311C4
cosocleC4×C311C24
hypercenterC22×C8D311
hypocenterC311C22×M16
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C22×C4 ◁ C22×C8

298 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, 1308);