Finite Group Databasebeta

C22×C4⋊(C71⋊C16) #32150427

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

Aliases

direct productC22×C4⋊(C71⋊C16)

Splittings

SylowC71 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C8C2×D71
commutatorC2×C71C23×C16
FrattiniC2×C8C23×D71
FittingC22×C4×C8×C71C2
socle, prime radicalC24×C71C2×C8
cosocleC2×C8×C71C24
hypercenterC22×C4×C8D71
hypocenterC71C22×C4⋊C16
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

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, 322543);