Finite Group Databasebeta

← Prev (#31995323) Next (#31995325) →

C2×C4×Dic71⋊C8 #31995324

order18176
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×Dic71⋊C8

Splittings

SylowC71 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC22×C42C2×D71
commutatorC2×C71C22×C4×C8
FrattiniC22×C4C23×D71
FittingC22×C4×C8×C71C2
socle, prime radicalC24×C71C22×C4
cosocleC22×C4×C71C24
hypercenterC22×C4×C8D71
hypocenterC71C2×C4×C4⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1550 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, 167440);