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C23×C29×Dic9 #37562143

order24012
automorphism?
homologyAbelianization (H1) = C4×C23×C29 · Schur multiplier (H2) = C1

Aliases

direct productC23×C29×Dic9
unambiguous semidirect productC9⋊(C4×C23×C29)

Splittings

derived, SylowC9 ⋊ C4×C23×C29
HallC9×C23×C29 ⋊ C4
HallC9×C29 ⋊ C4×C23
HallC9×C23 ⋊ C4×C29

Subgroups

subgroupG/H
center, hypercenterC2×C23×C29D9
commutator, hypocenterC9C4×C23×C29
FrattiniC2×C3D3×C23×C29
FittingC2×C9×C23×C29C2
socle, prime radicalC2×C3×C23×C29D3
cosocleC2×C9C2×C23×C29
LCSG ▷ C9
UCSC1 ◁ C2×C23×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24012

Conjugacy classes & character table

8004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 5);