Finite Group Databasebeta

← Prev (#35207938) Next (#35207940) →

C5×C23×Dic45 #35207939

order20700
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×Dic45
unambiguous semidirect productC9⋊(C5×Dic5×C23)

Splittings

derivedC5×C9 ⋊ C4×C5×C23
HallC52×C9×C23 ⋊ C4
HallC52×C23 ⋊ Dic9
HallC52×C9 ⋊ C4×C23
HallC9×C23 ⋊ C5×Dic5
SylowC52 ⋊ C23×Dic9
SylowC9 ⋊ C5×Dic5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D45
commutator, hypocenterC5×C9C4×C5×C23
FrattiniC2×C3C5×C23×D15
FittingC2×C52×C9×C23C2
socle, prime radicalC2×C3×C52×C23D3
cosocleC2×C5×C9C2×C5×C23
LCSG ▷ C5×C9
UCSC1 ◁ C2×C5×C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4140

Conjugacy classes & character table

5520 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 55);