Finite Group Databasebeta

← Prev (#39910721) Next (#39910723) →

C5×C23×Dic57 #39910722

order26220
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×Dic57
unambiguous semidirect productC3⋊(C5×C23×Dic19)
unambiguous semidirect productC19⋊(C5×Dic3×C23)

Splittings

derived, HallC3×C19 ⋊ C4×C5×C23
HallC3×C5×C19×C23 ⋊ C4
HallC5×C19×C23 ⋊ Dic3
HallC3×C19×C23 ⋊ C4×C5
HallC19×C23 ⋊ C5×Dic3
HallC3×C5×C23 ⋊ Dic19
HallC3×C5×C19 ⋊ C4×C23
HallC5×C19 ⋊ Dic3×C23
HallC3×C23 ⋊ C5×Dic19
SylowC19 ⋊ C5×Dic3×C23
HallC3×C5 ⋊ C23×Dic19
SylowC3 ⋊ C5×C23×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D57
commutator, hypocenterC3×C19C4×C5×C23
FrattiniC2C5×C23×D57
Fitting, socle, prime radicalC2×C3×C5×C19×C23C2
cosocleC2×C3×C19C2×C5×C23
LCSG ▷ C3×C19
UCSC1 ◁ C2×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26220

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 12);