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C3×Dic2057 #37590558

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

Aliases

direct productC3×Dic2057
unambiguous semidirect productC121⋊(C3×Dic17)

Splittings

derived, HallC17×C121 ⋊ C3×C4
HallC3×C17×C121 ⋊ C4
HallC3×C121 ⋊ Dic17
SylowC121 ⋊ C3×Dic17
HallC3×C17 ⋊ Dic121
SylowC17 ⋊ C3×Dic121

Subgroups

subgroupG/H
center, hypercenterC2×C3D2057
commutator, hypocenterC17×C121C3×C4
FrattiniC2×C11C3×D187
FittingC2×C3×C17×C121C2
socle, prime radicalC2×C3×C11×C17D11
cosocleC2×C17×C121C2×C3
LCSG ▷ C17×C121
UCSC1 ◁ C2×C3

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24684

Conjugacy classes & character table

6180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 4);