Finite Group Databasebeta

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C2×C32×D13×C11⋊C5 #38788117

order25740
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D13×C11⋊C5
unambiguous semidirect product(C2×C32×C11×D13)⋊C5

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2×C5
derived, HallC11×C13 ⋊ C22×C32×C5
HallC32×C13×C11⋊C5 ⋊ C22
HallC2×C32×C11×D13 ⋊ C5
HallC32×C11×C13 ⋊ C22×C5
HallC13×C11⋊C5 ⋊ C22×C32
HallC2×C11×D13 ⋊ C32×C5
HallC32×C13 ⋊ C22×C11⋊C5
HallC32×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C22×C32×C11⋊C5
SylowC11 ⋊ C2×C32×C5×D13

Subgroups

subgroupG/H
center, hypercenterC2×C32D13×C11⋊C5
commutator, cosocle, hypocenterC11×C13C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2×C32

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2574

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 348);