Finite Group Databasebeta

C2×C4×C71⋊#95 #31918521

order18176
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×C71⋊#95

Splittings

SylowC71 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC24×C4C2×D71
commutatorC2×C71C2×C43
FrattiniC24C23×D71
FittingC23×C42×C71C2
socle, prime radicalC25×C71C23
cosocleC24×C71C24
hypercenterC23×C42D71
hypocenterC71C2×C4×#95
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C24×C4 ◁ C23×C42

4462 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, 90637);