Finite Group Databasebeta

C2×#22589519 #32024897

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22589519

Splittings

SylowC71 ⋊ C2×#2033

Subgroups

subgroupG/H
centerC24C2×C22⋊D71
commutator, cosocleC22×C4×C71C24
FrattiniC22×C4C23×D71
Fitting, prime radicalC22×#121×C71C2
socleC24×C71C2×D4
hypercenterC22×#121D71
hypocenterC71C2×#2033
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 197013);