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C9×C23×#1044 #35208011

order20700
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C5

Aliases

direct productC9×C23×#1044

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#1044
commutator, hypocenterC52C4×C9×C23
FrattiniC3C3×C23×#1044
FittingC52×C9×C23C4
socleC3×C52×C23C3×C4
prime radicalC3×C23×C5⋊D5C2×C3
cosocleC3×C5⋊D5C2×C3×C23
LCSG ▷ C52
UCSC1 ◁ C9×C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2070

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 127);