Finite Group Databasebeta

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C4×C5×C11×#3861 #44568515

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C11×#3861

Splittings

Fitting, HallC4×C5×C72×C11 ⋊ C3
derived, SylowC72 ⋊ C3×C4×C5×C11
HallC5×C72×C11 ⋊ C3×C4
HallC4×C72×C11 ⋊ C3×C5
HallC4×C5×C72 ⋊ C3×C11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C11
HallC4×C72 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC4×C5×C11#3861
commutator, hypocenterC72C3×C4×C5×C11
FrattiniC2C2×C5×C11×#3861
FittingC4×C5×C72×C11C3
socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3861C2
cosocleC2×C72C2×C3×C5×C11
LCSG ▷ C72
UCSC1 ◁ C4×C5×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

4180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 217);