Finite Group Databasebeta

C22×#10622202 #14906649

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

Aliases

direct productC22×#10622202

Splittings

SylowC11 ⋊ C22×#358

Subgroups

subgroupG/H
centerC24#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC23×C11×Q16C2
socle, prime radicalC24×C11D8
cosocleC2×C8×C11C24
hypercenterC23×Q16D11
hypocenterC11C22×#358
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×Q16

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 322444);