Finite Group Databasebeta

C2×C4⋊Dic619 #34090308

order19808
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic619

Splittings

SylowC619 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D619
commutatorC2×C619C22×C4
FrattiniC22C22×D619
FittingC22×C4×C619C2
socle, prime radicalC23×C619C22
cosocleC22×C619C23
hypercenterC22×C4D619
hypocenterC619C2×C4⋊C4
LCSG ▷ C2×C619 ▷ C619
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19808

Conjugacy classes & character table

4964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19808, 101);