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C11×#14556844 #38788152

order25740
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×#14556844

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C5×C13 ⋊ C4×C11
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ #157
HallC32×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ #4380
HallC32×C13 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ #63120
HallC5×C13 ⋊ C11×#157
HallC5×C11 ⋊ #90865
HallC32×C5 ⋊ C11×Dic13
SylowC13 ⋊ C11×#4380
SylowC32 ⋊ C11×#63120
SylowC5 ⋊ C11×#90865

Subgroups

subgroupG/H
center, hypercenterC11#14556844
commutator, hypocenterC32×C5×C13C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC11×C13×C3⋊D15C2
cosocleC13×C3⋊D15C2×C11
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

1749 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 383);