Finite Group Databasebeta

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C2×C3×D17×C121 #37590582

order24684
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D17×C121
unambiguous semidirect productC17⋊(C22×C3×C121)
unambiguous semidirect product(C2×C17)⋊(C2×C3×C121)

Splittings

FittingC2×C3×C17×C121 ⋊ C2
derived, SylowC17 ⋊ C22×C3×C121
HallC3×C17×C121 ⋊ C22
HallC17×C121 ⋊ C22×C3
HallC3×C17 ⋊ C22×C121

Subgroups

subgroupG/H
center, hypercenterC2×C3×C121D17
commutator, hypocenterC17C22×C3×C121
FrattiniC11C2×C3×C11×D17
FittingC2×C3×C17×C121C2
socleC2×C3×C11×C17C2×C11
prime radicalC2×C3×C11×D17C11
cosocleC11×C17C22×C3×C11
LCSG ▷ C17
UCSC1 ◁ C2×C3×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12342

Conjugacy classes & character table

7260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 28);