Finite Group Databasebeta

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C3×Dic2695 #44568309

order32340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2695
unambiguous semidirect productC11⋊(C3×Dic245)

Splittings

derived, HallC5×C11×C49 ⋊ C3×C4
HallC3×C5×C11×C49 ⋊ C4
HallC3×C11×C49 ⋊ Dic5
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ C3×Dic5
HallC5×C49 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ Dic55
HallC5×C11 ⋊ C3×Dic49
SylowC49 ⋊ C3×Dic55
HallC3×C11 ⋊ Dic245
HallC3×C5 ⋊ Dic539
SylowC11 ⋊ C3×Dic245
SylowC5 ⋊ C3×Dic539

Subgroups

subgroupG/H
center, hypercenterC2×C3D2695
commutator, hypocenterC5×C11×C49C3×C4
FrattiniC2×C7C3×D385
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11D7
cosocleC2×C5×C11×C49C2×C3
LCSG ▷ C5×C11×C49
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 11);