Finite Group Databasebeta

C23×Dic19⋊C4 #14576795

order2432
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×Dic19⋊C4

Splittings

SylowC19 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC25C2×D19
commutatorC2×C19C24×C4
FrattiniC22C24×D19
FittingC24×C4×C19C2
socle, prime radicalC25×C19C22
cosocleC22×C19C25
hypercenterC24×C4D19
hypocenterC19C23×C4⋊C4
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C25 ◁ C24×C4

2488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

Relationships

maximal subgroup of#18070465, #18073868
maximal normal subgroup of#18070465, #18073868

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 17670);