Finite Group Databasebeta

C2×#14561534 #18072795

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14561534

Splittings

SylowC19 ⋊ C2×#1302

Subgroups

subgroupG/H
centerC22×C4(C2×D19)⋊C4
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC22×C19×#97C2
socleC23×C19#95
prime radicalC24×C19C4⋊C4
cosocleC2×C42×C19C23
hypercenterC22×#97D19
hypocenterC19C2×#1302
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2432

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59824);