Finite Group Databasebeta

C2×#13077206 #15617434

order2816
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13077206

Splittings

SylowC11 ⋊ C2×#2911

Subgroups

subgroupG/H
centerC22×C4C2×D44
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC23×C11×M16C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC2×C4×C11C25
hypercenterC23×M16D11
hypocenterC11C2×#2911
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033229);