Finite Group Databasebeta

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C5×C11×#10596875 #44568476

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C7

Aliases

direct productC5×C11×#10596875

Splittings

derived, SylowC72 ⋊ C3×C4×C5×C11
HallC5×C11×C7⋊Dic7 ⋊ C3
HallC5×C11×#3862 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC11×C7⋊Dic7 ⋊ C3×C5
HallC11×#3862 ⋊ C4×C5
HallC5×C7⋊Dic7 ⋊ C3×C11
HallC5×#3862 ⋊ C4×C11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C11
HallC7⋊Dic7 ⋊ C3×C5×C11
Hall#3862 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11#64425
commutator, hypocenterC72C3×C4×C5×C11
FrattiniC2C5×C11×#64425
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C72C2×C3×C5×C11
LCSG ▷ C72
UCSC1 ◁ C2×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 178);