Finite Group Databasebeta

← Prev (#35208012) Next (#35208014) →

C9×C23×#1042 #35208013

order20700
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×#1042

Splittings

Fitting, HallC52×C9×C23 ⋊ C4
derived, SylowC52 ⋊ C4×C9×C23
HallC52×C23 ⋊ C4×C9
HallC52×C9 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC9×C23#1042
commutator, hypocenterC52C4×C9×C23
FrattiniC3C3×C23×#1042
FittingC52×C9×C23C4
socleC3×C52×C23C3×C4
prime radicalC3×C5×D5×C23C2×C3
cosocleC3×C5×D5C2×C3×C23
LCSG ▷ C52
UCSC1 ◁ C9×C23

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4140

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 129);