Finite Group Databasebeta

C2×#13070768 #14908402

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

Aliases

direct productC2×#13070768

Splittings

SylowC11 ⋊ C2×#2227

Subgroups

subgroupG/H
centerC23C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×Q16C2
socle, prime radicalC23×C11C2×D8
hypercenterC2×C4×Q16D11
hypocenterC11C2×#2227
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 324197);