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C11×#14556846 #38788158

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

Aliases

direct productC11×#14556846

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C5×C13 ⋊ C4×C11
HallC32×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ #157
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ #4379
HallC32×C13 ⋊ C11×Dic5
HallC32×C11 ⋊ #63118
HallC5×C13 ⋊ C11×#157
HallC5×C11 ⋊ #90866
HallC32×C5 ⋊ C11×#261
SylowC13 ⋊ C11×#4379
SylowC32 ⋊ C11×#63118
SylowC5 ⋊ C11×#90866

Subgroups

subgroupG/H
center, hypercenterC11#14556846
commutator, hypocenterC32×C5×C13C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC5×C11×C3⋊D39C2
cosocleC5×C3⋊D39C2×C11
LCSG ▷ C32×C5×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 389);