Finite Group Databasebeta

C2×C4×Dic622 #34092159

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

Aliases

direct productC2×C4×Dic622

Splittings

SylowC311 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D311
commutatorC2×C311C23×C4
FrattiniC22C23×D311
FittingC2×C42×C311C2
socle, prime radicalC23×C311C23
cosocleC22×C311C24
hypercenterC2×C42D311
hypocenterC311C2×C4×Q8
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C22×C4 ◁ C2×C42

298 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, 1014);