Finite Group Databasebeta

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C4×C11×C61⋊C9 #37563444

order24156
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×C61⋊C9
unambiguous semidirect product(C4×C61)⋊(C9×C11)
unambiguous semidirect product(C4×C11×C61)⋊C9

Splittings

derived, SylowC61 ⋊ C4×C9×C11
HallC4×C11×C61 ⋊ C9
HallC11×C61 ⋊ C4×C9
HallC4×C61 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11C61⋊C3
commutator, hypocenterC61C4×C9×C11
FrattiniC2×C3C2×C11×C61⋊C3
FittingC3×C4×C11×C61C3
socle, prime radicalC2×C3×C11×C61C2×C3
cosocleC2×C3×C61C2×C3×C11
LCSG ▷ C61
UCSC1 ◁ C3×C4×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24156

Conjugacy classes & character table

3036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 2);