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#100×C22⋊D11 #14769121

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#100×C22⋊D11

Splittings

FittingC22×C11×#100 ⋊ C2
SylowC11 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#100C2
socleC22×C11C22×C22⋊C4
prime radicalC2×D4×C22⋊D11C2
cosocleC22×C4×C11C24
hypercenterC22×#100D11
hypocenterC11D4×#100
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 184916);