Finite Group Databasebeta

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C2×C32×C5×C11×D13 #38788301

order25740
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×C11×D13

Splittings

Fitting, socleC2×C32×C5×C11×C13 ⋊ C2
derived, SylowC13 ⋊ C22×C32×C5×C11
HallC32×C5×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C22×C32
HallC32×C5×C13 ⋊ C22×C11
HallC11×C13 ⋊ C22×C32×C5
HallC32×C13 ⋊ C22×C5×C11
HallC5×C13 ⋊ C22×C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C11D13
commutator, cosocle, hypocenterC13C22×C32×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C13
UCSC1 ◁ C2×C32×C5×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12870

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 532);