Finite Group Databasebeta

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C3×Dic17×C121 #37590556

order24684
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic17×C121

Splittings

derived, SylowC17 ⋊ C3×C4×C121
HallC3×C17×C121 ⋊ C4
HallC17×C121 ⋊ C3×C4
HallC3×C17 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C3×C121D17
commutator, hypocenterC17C3×C4×C121
FrattiniC2×C11C3×C11×D17
FittingC2×C3×C17×C121C2
socle, prime radicalC2×C3×C11×C17C2×C11
cosocleC2×C11×C17C2×C3×C11
LCSG ▷ C17
UCSC1 ◁ C2×C3×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24684

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, 2);