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C9×Dic11×C61 #37563446

order24156
automorphism?
homologyAbelianization (H1) = C4×C9×C61 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic11×C61
unambiguous semidirect productC11⋊(C4×C9×C61)

Splittings

derived, SylowC11 ⋊ C4×C9×C61
HallC9×C11×C61 ⋊ C4
HallC11×C61 ⋊ C4×C9
HallC9×C11 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC2×C9×C61D11
commutator, hypocenterC11C4×C9×C61
FrattiniC2×C3C3×D11×C61
FittingC2×C9×C11×C61C2
socle, prime radicalC2×C3×C11×C61C2×C3
cosocleC2×C3×C11C2×C3×C61
LCSG ▷ C11
UCSC1 ◁ C2×C9×C61

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24156

Conjugacy classes & character table

7686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 4);