Finite Group Databasebeta

C2×#13066709 #14668659

order2816
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13066709

Splittings

SylowC11 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC22×C4#4323
commutatorC8×C11C2×C42
FrattiniC22×C8C22×D11
FittingC22×C11×#108C2
socleC23×C11#107
prime radicalC24×C11Q16
cosocleC22×C8×C11C23
hypercenterC22×#108D11
hypocenterC11C2×#1381
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 84454);