Finite Group Databasebeta

← Prev (#39910712) Next (#39910714) →

C3×C5×C19×Dic23 #39910713

order26220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C19×Dic23
unambiguous semidirect productC23⋊(C3×C4×C5×C19)

Splittings

derived, SylowC23 ⋊ C3×C4×C5×C19
HallC3×C5×C19×C23 ⋊ C4
HallC5×C19×C23 ⋊ C3×C4
HallC3×C19×C23 ⋊ C4×C5
HallC19×C23 ⋊ C3×C4×C5
HallC3×C5×C23 ⋊ C4×C19
HallC5×C23 ⋊ C3×C4×C19
HallC3×C23 ⋊ C4×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C19D23
commutator, hypocenterC23C3×C4×C5×C19
FrattiniC2C3×C5×C19×D23
Fitting, socle, prime radicalC2×C3×C5×C19×C23C2
cosocleC2×C23C2×C3×C5×C19
LCSG ▷ C23
UCSC1 ◁ C2×C3×C5×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26220

Conjugacy classes & character table

7410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 3);