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C29×Dic207 #37562145

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

Aliases

direct productC29×Dic207
unambiguous semidirect productC9⋊(C29×Dic23)
unambiguous semidirect productC23⋊(C29×Dic9)

Splittings

derived, HallC9×C23 ⋊ C4×C29
HallC9×C23×C29 ⋊ C4
HallC23×C29 ⋊ Dic9
HallC9×C29 ⋊ Dic23
SylowC23 ⋊ C29×Dic9
SylowC9 ⋊ C29×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C29D207
commutator, hypocenterC9×C23C4×C29
FrattiniC2×C3C29×D69
FittingC2×C9×C23×C29C2
socle, prime radicalC2×C3×C23×C29D3
cosocleC2×C9×C23C2×C29
LCSG ▷ C9×C23
UCSC1 ◁ C2×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24012

Conjugacy classes & character table

6090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 7);