Finite Group Databasebeta

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C3×C17×Dic121 #37590557

order24684
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic121
unambiguous semidirect productC121⋊(C3×C4×C17)

Splittings

derived, SylowC121 ⋊ C3×C4×C17
HallC3×C17×C121 ⋊ C4
HallC17×C121 ⋊ C3×C4
HallC3×C121 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D121
commutator, hypocenterC121C3×C4×C17
FrattiniC2×C11C3×C17×D11
FittingC2×C3×C17×C121C2
socle, prime radicalC2×C3×C11×C17D11
cosocleC2×C121C2×C3×C17
LCSG ▷ C121
UCSC1 ◁ C2×C3×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24684

Conjugacy classes & character table

6324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 3);