Finite Group Databasebeta

C4×#95×D71 #31918519

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

Aliases

direct productC4×#95×D71

Splittings

FittingC4×#95×C71 ⋊ C2
SylowC71 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC2×C71C2×C43
FrattiniC24C23×D71
FittingC4×#95×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC4×#95D71
hypocenterC71C2×C4×#95
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C4×#95

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 90635);