Finite Group Databasebeta

C22⋊C4×D607 #34085334

order19424
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D607

Splittings

FittingC22⋊C4×C607 ⋊ C2
SylowC607 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D607
commutatorC2×C607C22×C4
FittingC22⋊C4×C607C2
socle, cosocleC22×C607C23
prime radicalC23×D607C2
hypercenterC22⋊C4D607
hypocenterC607C2×C22⋊C4
LCSG ▷ C2×C607 ▷ C607
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4856

Conjugacy classes & character table

3050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19424, 96);