Finite Group Databasebeta

C22×(C2×D71)⋊C16 #32150116

order18176
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D71)⋊C16

Splittings

FittingC23×C16×C71 ⋊ C2
SylowC71 ⋊ C22×C22⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D71
commutatorC2×C71C23×C16
FrattiniC2×C8C23×D71
FittingC23×C16×C71C2
socleC24×C71C2×C8
prime radicalC24×D71C8
cosocleC2×C8×C71C24
hypercenterC23×C16D71
hypocenterC71C22×C22⋊C16
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 322232);