Finite Group Databasebeta

C2×#22601422 #32878475

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22601422

Splittings

SylowC71 ⋊ C2×#3402

Subgroups

subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#495×C71C2
socleC23×C71C22×D4
prime radicalC22×D8×C71C22
hypercenterC2×#495D71
hypocenterC71C2×#3402
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

1938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1598 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1050591);