Finite Group Databasebeta

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C5×Dic11×#3861 #44568484

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

Aliases

direct productC5×Dic11×#3861

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC5×C72×Dic11 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC72×Dic11 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC5×C72 ⋊ C3×Dic11
HallC5×C11 ⋊ C4×#3861
SylowC72 ⋊ C3×C5×Dic11
SylowC11 ⋊ C4×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC2×C5D11×#3861
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C5×D11×#3861
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3861C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 186);