Finite Group Databasebeta

C22×Dic599⋊C4 #50306340

order38336
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×Dic599⋊C4

Splittings

SylowC599 ⋊ C22×C4⋊C4

Subgroups

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

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38336

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, 999);