Finite Group Databasebeta

C2×#10589415 #11795955

order1152
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C24×C3

Aliases

direct productC2×#10589415

Splittings

SylowC32 ⋊ C2×C22⋊C16

Subgroups

subgroupG/H
centerC22×C8C2×C3⋊D3
commutatorC2×C32C22×C16
FrattiniC2×C8C22×C3⋊D3
FittingC23×C32×C8C2
socleC23×C32C2×C8
prime radicalC24×C32C8
cosocleC2×C32×C8C23
hypercenterC23×C8C3⋊D3
hypocenterC32C2×C22⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C8 ◁ C23×C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 29966);