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C9×C23×#1181 #37562148

order24012
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×#1181

Splittings

Fitting, HallC9×C23×C29 ⋊ C4
derived, SylowC29 ⋊ C4×C9×C23
HallC23×C29 ⋊ C4×C9
HallC9×C29 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC9×C23#1181
commutator, hypocenterC29C4×C9×C23
FrattiniC3C3×C23×#1181
FittingC9×C23×C29C4
socleC3×C23×C29C3×C4
prime radicalC3×C23×D29C2×C3
cosocleC3×D29C2×C3×C23
LCSG ▷ C29
UCSC1 ◁ C9×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6003

Conjugacy classes & character table

2277 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 10);