Finite Group Databasebeta

C22⋊C4×D617 #34089652

order19744
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D617

Splittings

FittingC22⋊C4×C617 ⋊ C2
SylowC617 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D617
commutatorC2×C617C22×C4
FittingC22⋊C4×C617C2
socle, cosocleC22×C617C23
prime radicalC23×D617C2
hypercenterC22⋊C4D617
hypocenterC617C2×C22⋊C4
LCSG ▷ C2×C617 ▷ C617
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4936

Conjugacy classes & character table

3100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19744, 96);