Finite Group Databasebeta

C2×(C22⋊D71)⋊C16 #32150599

order18176
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D71)⋊C16

Splittings

FittingC2×C22⋊C16×C71 ⋊ C2
SylowC71 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C8C22×D71
commutatorC2×C71C23×C16
FrattiniC2×C8C23×D71
FittingC2×C22⋊C16×C71C2
socleC23×C71C22×C8
prime radicalC22×C22⋊D71C8
cosocleC2×C8×C71C24
hypercenterC2×C22⋊C16D71
hypocenterC71C2×D4×C16
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 322715);