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Dic3×C17×C121 #37590559

order24684
automorphism?
homologyAbelianization (H1) = C4×C17×C121 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C17×C121
unambiguous semidirect productC3⋊(C4×C17×C121)

Splittings

derived, SylowC3 ⋊ C4×C17×C121
HallC3×C17×C121 ⋊ C4
HallC3×C121 ⋊ C4×C17
HallC3×C17 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C17×C121D3
commutator, hypocenterC3C4×C17×C121
FrattiniC2×C11D3×C11×C17
FittingC2×C3×C17×C121C2
socle, prime radicalC2×C3×C11×C17C2×C11
cosocleC2×C3×C11C2×C11×C17
LCSG ▷ C3
UCSC1 ◁ C2×C17×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24684

Conjugacy classes & character table

12342 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 5);