Finite Group Databasebeta

C2×#22586439 #31912353

order18176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22586439

Splittings

SylowC71 ⋊ C2×#1383

Subgroups

subgroupG/H
centerC23#14556060
commutatorC8×C71C2×C42
FrattiniC22×C8C22×D71
FittingC22×M32×C71C2
socleC23×C71#106
prime radicalC24×C71SD16
cosocleC22×C8×C71C23
hypercenterC22×M32D71
hypocenterC71C2×#1383
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2864 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 84469);