Finite Group Databasebeta

C2×#22586239 #31887708

order18176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#22586239

Splittings

SylowC71 ⋊ C2×#1302

Subgroups

subgroupG/H
centerC22×C4(C2×D71)⋊C4
commutatorC2×C4×C71C2×C42
FrattiniC2×C42C22×D71
FittingC22×#97×C71C2
socleC23×C71#95
prime radicalC24×C71C4⋊C4
cosocleC2×C42×C71C23
hypercenterC22×#97D71
hypocenterC71C2×#1302
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 59824);