Finite Group Databasebeta

C23×Dic622 #34092518

order19904
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic622

Splittings

SylowC311 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC24C2×D311
commutator, cosocleC2×C311C25
FrattiniC2C24×D311
FittingC23×C4×C311C2
socle, prime radicalC24×C311C22
hypercenterC23×C4D311
hypocenterC311C23×Q8
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C24 ◁ C23×C4

850 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, 1373);