Finite Group Databasebeta

C2×C4⋊(C3⋊(C3⋊C16)) #11796972

order1152
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C4⋊(C3⋊(C3⋊C16))

Splittings

SylowC32 ⋊ C2×C4⋊C16

Subgroups

subgroupG/H
centerC22×C8C2×C3⋊D3
commutatorC2×C32C22×C16
FrattiniC2×C8C22×C3⋊D3
FittingC2×C32×C4×C8C2
socle, prime radicalC23×C32C2×C8
cosocleC2×C32×C8C23
hypercenterC2×C4×C8C3⋊D3
hypocenterC32C2×C4⋊C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

552 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, 30983);