Finite Group Databasebeta

C23×(C22⋊D11)⋊C4 #15660335

order2816
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×(C22⋊D11)⋊C4

Splittings

FittingC23×C11×C22⋊C4 ⋊ C2
SylowC11 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC25C22×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC23×C11×C22⋊C4C2
socleC25×C11C23
prime radicalC24×C22⋊D11C2
cosocleC22×C11C26
hypercenterC23×C22⋊C4D11
hypocenterC11C23×C4×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C25 ◁ C23×C22⋊C4

19998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076130);