Finite Group Databasebeta

C2×#22589177 #32001197

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#22589177

Splittings

SylowC71 ⋊ C2×#1964

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
Fitting, prime radicalC22×#121×C71C2
socleC23×C71C2×C22⋊C4
cosocleC24×C71C24
hypercenterC22×#121D71
hypocenterC71C2×#1964
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

2218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

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, 173313);