Finite Group Databasebeta

C2×#22602943 #32904837

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22602943

Splittings

SylowC71 ⋊ C2×#3563

Subgroups

subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#529×C71C2
socleC23×C71C25
prime radicalC2×#121×C71C22
hypercenterC2×#529D71
hypocenterC71C2×#3563
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#529

6458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076953);