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C32×C13×C11⋊AGL(1,𝔽5) #38788170

order25740
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C13×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C32×C13×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC5×C11 ⋊ C32×C4×C13
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ C32×C4
HallC32×C5×C13 ⋊ Dic11
HallC32×C5×C11 ⋊ C4×C13
HallC11×C13 ⋊ C32×AGL(1,𝔽5)
HallC32×C11 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ C32×Dic11
HallC32×C5 ⋊ C13×Dic11
SylowC11 ⋊ C32×C13×AGL(1,𝔽5)
SylowC5 ⋊ C32×C13×Dic11

Subgroups

subgroupG/H
center, hypercenterC32×C13C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C32×C4×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×D5×C11×C13C2
cosocleD5×C11C2×C32×C13
LCSG ▷ C5×C11
UCSC1 ◁ C32×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 401);