Finite Group Databasebeta

← Prev (#34089654) Next (#34089656) →

C4⋊C4×D617 #34089655

order19744
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C4×D617

Splittings

FittingC4⋊C4×C617 ⋊ C2
SylowC617 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D617
commutatorC2×C617C22×C4
FittingC4⋊C4×C617C2
socle, cosocleC22×C617C23
prime radicalC22×D617C22
hypercenterC4⋊C4D617
hypocenterC617C2×C4⋊C4
LCSG ▷ C2×C617 ▷ C617
UCSC1 ◁ C22 ◁ C4⋊C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9872

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, 99);