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C22×C11×C13×C11⋊C5 #44538225

order31460
automorphism?
homologyAbelianization (H1) = C22×C5×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×C13×C11⋊C5
unambiguous semidirect product(C22×C11)⋊(C5×C11×C13)
unambiguous semidirect product(C22×C11×C13)⋊(C5×C11)

Splittings

Fitting, socle, HallC22×C112×C13 ⋊ C5
derivedC11 ⋊ C22×C5×C11×C13
HallC112×C13 ⋊ C22×C5
HallC22×C112 ⋊ C5×C13
SylowC112 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC22×C11×C13C11⋊C5
commutator, cosocle, hypocenterC11C22×C5×C11×C13
FrattiniC1G
Fitting, socleC22×C112×C13C5
LCSG ▷ C11
UCSC1 ◁ C22×C11×C13

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

4004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 165);