Finite Group Databasebeta

C22×(C2×D599)⋊C4 #50306337

order38336
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D599)⋊C4

Splittings

FittingC23×C4×C599 ⋊ C2
SylowC599 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D599
commutatorC2×C599C23×C4
FrattiniC22C23×D599
FittingC23×C4×C599C2
socleC24×C599C22
prime radicalC24×D599C2
cosocleC22×C599C24
hypercenterC23×C4D599
hypocenterC599C22×C22⋊C4
LCSG ▷ C2×C599 ▷ C599
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19168

Conjugacy classes & character table

9608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38336, 996);