Finite Group Databasebeta

C2×(C2×D71)⋊#95 #31918540

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×(C2×D71)⋊#95

Splittings

FittingC22×#95×C71 ⋊ C2
SylowC71 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC25C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC22×#95×C71C2
socleC25×C71C23
prime radicalC25×D71C22
cosocleC24×C71C24
hypercenterC22×#95D71
hypocenterC71C2×C22⋊#95
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C25 ◁ C22×#95

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 90656);