Finite Group Databasebeta

C2×C4⋊(C9⋊C16) #11796971

order1152
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊(C9⋊C16)

Splittings

SylowC9 ⋊ C2×C4⋊C16

Subgroups

subgroupG/H
centerC22×C8C2×D9
commutatorC2×C9C22×C16
FrattiniC2×C3×C8C22×D3
FittingC2×C4×C8×C9C2
socle, prime radicalC23×C3C2×C3⋊C8
cosocleC2×C8×C9C23
hypercenterC2×C4×C8D9
hypocenterC9C2×C4⋊C16
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

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, 30982);